From 56b73e96d4bad2950bf97a94f6555abc125e0aa6 Mon Sep 17 00:00:00 2001 From: Michael Denes Date: Wed, 29 Jul 2026 14:45:42 +0200 Subject: [PATCH 01/17] Preliminary grids explanation (need to rename images and move elsewhere) --- docs/user_guide/examples/explanation_grids.md | 41 ++++++++++++++---- docs/user_guide/examples/image-1.png | Bin 0 -> 41574 bytes docs/user_guide/examples/image-2.png | Bin 0 -> 111353 bytes docs/user_guide/examples/image-3.png | Bin 0 -> 31432 bytes docs/user_guide/examples/image-4.png | Bin 0 -> 32374 bytes docs/user_guide/examples/image-5.png | Bin 0 -> 65515 bytes docs/user_guide/examples/image.png | Bin 0 -> 95840 bytes 7 files changed, 33 insertions(+), 8 deletions(-) create mode 100644 docs/user_guide/examples/image-1.png create mode 100644 docs/user_guide/examples/image-2.png create mode 100644 docs/user_guide/examples/image-3.png create mode 100644 docs/user_guide/examples/image-4.png create mode 100644 docs/user_guide/examples/image-5.png create mode 100644 docs/user_guide/examples/image.png diff --git a/docs/user_guide/examples/explanation_grids.md b/docs/user_guide/examples/explanation_grids.md index 61484bdbf0..8943a86112 100644 --- a/docs/user_guide/examples/explanation_grids.md +++ b/docs/user_guide/examples/explanation_grids.md @@ -1,10 +1,35 @@ # 📖 Grids -Parcels `Field` objects exist on a (structured) `parcels.XGrid` or (unstructured) `parcels.Uxgrid`. Here we describe these grids on a conceptual level. - -```{note} -The contents for this page are still under development in v4. -TODO -- link to xgcm.Grid documentation -- adapt from v3 grid indexing tutorial (../examples_v3/documentation_indexing.ipynb) -``` +In Lagrangian ocean analysis, virtual particle tracking requires the accurate interpolation of physical properties (flow velocities and tracer properties) to particle locations. The underlying data that forces the particle movement will likely be defined on a discretised grid. Parcels can natively handle two styles of grids; structured and unstructured, where parcels `Field` objects exist on a (structured) `parcels.XGrid` or (unstructured) `parcels.Uxgrid`. Here we describe these grids on a conceptual level. + +## Structured grids +A structured grid is composed of quadrilateral elements, that are indexed using logical 2D or 3D indices, like $(i,j,k)$. In `xarray` terminology, these indices correspond to `dimensions`, for example [...]. In structured grids, grid cell neighbours are easily found by decrementing or incrementing these dimensions. + +There are two styles of structured grids, rectilinear and curvilinear, as shown in Figure 1. Rectilinear grids are nearly always aligned with the coordinate axes (that is, there is a one-to-one mapping between the dimensions and the physical coordinate space), making them simple and computationally efficient to query. However, they're limited by the fact that it is difficult to resolve complex coastlines without high resolution, and they suffer from singularities in the flow fields at the poles where the grid lines converge. Curvilinear grids allow for curved grid lines, which allow for better representation of coastlines. They often move the poles onto land to avoid singularities occuring in the ocean. However, they become trickier to work with, as the spatial positions of their vertices are stored in separate 2D arrays, and moving to an eastward neighbour is not as simple as incrementing the $i$-th coordinate by 1. + +![Figure 1 from parcels v2 paper](image.png) + + +## Unstructured grids +TODO: For Joe. + + +## How your data may be defined +Regardless of your grid type, how your data is defined on your grid is equally important. Here, we will describe how you can interpret your data at a very general level, and the concept applies for any $n$-gon ($n$-sided polygon with $n \ge 3$). + +### Nodes, edges, and faces +Let's assume we have a simple 2D rectlinear grid. The grid is composed of a number of nodes (or vertices), connected by edges, which together construct grid cells and grid cell faces. In Figure 2, we draw a simple grid cell. Here, your data may be defined on the corners of the grid cell (the nodes/vertices), at the centre of the cell face, or across a cell edge. + +![Figure 2 - A simple grid cell. Blue circles denote nodes (or vertices) of the grid cell. The red circle denotes the centre of the cell face.](image-1.png) + +You will need to make several assumptions about your data. Your data may represent a point-wise "sample" of some field. For example, velocity data may be defined at the nodes of your grid, and a fairly safe assumption to make is that you can bi-linearly interpolate these data points to your particle positions. In such an example, your velocity field may look like Figure 3. + +![Figure 3 - Bi-linear interpolation of point-wise data at nodes](image-2.png) + +Alternatively, your data may represent an "average value" across a cell face. For example, your temperature and salinity data may be defined at the cell centre, and represent an average value for the entire grid cell. A fairly safe assumption to make is that you can nearest-neighbour interpolate these data points to your particle positions. In such a case, your temperature field may look like figure 4. + +![Figure 4 - Nearest-neighbour interpolation of "grid cell averaged" data at cell centres](image-4.png) + +Lastly, your data may represent a value across a cell edge. For example, in (2D) Arakawa C-grid datasets, velocities are defined across an edge as they represent a "flux" across that cell edge. [for some reason an accepted assumption is] to perform a 1D linear interpolation of the zonal velocity in the zonal direction, and similarly a 1D linear interpolation of the meridional velocity in the meridional direction. 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Subject: [PATCH 04/17] [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci --- docs/user_guide/examples/explanation_grids.md | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/docs/user_guide/examples/explanation_grids.md b/docs/user_guide/examples/explanation_grids.md index 8943a86112..f6292631df 100644 --- a/docs/user_guide/examples/explanation_grids.md +++ b/docs/user_guide/examples/explanation_grids.md @@ -3,21 +3,23 @@ In Lagrangian ocean analysis, virtual particle tracking requires the accurate interpolation of physical properties (flow velocities and tracer properties) to particle locations. The underlying data that forces the particle movement will likely be defined on a discretised grid. Parcels can natively handle two styles of grids; structured and unstructured, where parcels `Field` objects exist on a (structured) `parcels.XGrid` or (unstructured) `parcels.Uxgrid`. Here we describe these grids on a conceptual level. ## Structured grids + A structured grid is composed of quadrilateral elements, that are indexed using logical 2D or 3D indices, like $(i,j,k)$. In `xarray` terminology, these indices correspond to `dimensions`, for example [...]. In structured grids, grid cell neighbours are easily found by decrementing or incrementing these dimensions. There are two styles of structured grids, rectilinear and curvilinear, as shown in Figure 1. Rectilinear grids are nearly always aligned with the coordinate axes (that is, there is a one-to-one mapping between the dimensions and the physical coordinate space), making them simple and computationally efficient to query. However, they're limited by the fact that it is difficult to resolve complex coastlines without high resolution, and they suffer from singularities in the flow fields at the poles where the grid lines converge. Curvilinear grids allow for curved grid lines, which allow for better representation of coastlines. They often move the poles onto land to avoid singularities occuring in the ocean. However, they become trickier to work with, as the spatial positions of their vertices are stored in separate 2D arrays, and moving to an eastward neighbour is not as simple as incrementing the $i$-th coordinate by 1. ![Figure 1 from parcels v2 paper](image.png) - ## Unstructured grids -TODO: For Joe. +TODO: For Joe. ## How your data may be defined + Regardless of your grid type, how your data is defined on your grid is equally important. Here, we will describe how you can interpret your data at a very general level, and the concept applies for any $n$-gon ($n$-sided polygon with $n \ge 3$). ### Nodes, edges, and faces + Let's assume we have a simple 2D rectlinear grid. The grid is composed of a number of nodes (or vertices), connected by edges, which together construct grid cells and grid cell faces. In Figure 2, we draw a simple grid cell. Here, your data may be defined on the corners of the grid cell (the nodes/vertices), at the centre of the cell face, or across a cell edge. ![Figure 2 - A simple grid cell. Blue circles denote nodes (or vertices) of the grid cell. The red circle denotes the centre of the cell face.](image-1.png) From f81176d74d0034dd259c739040d3059a3c589bf4 Mon Sep 17 00:00:00 2001 From: Erik van Sebille Date: Wed, 29 Jul 2026 17:35:53 +0200 Subject: [PATCH 05/17] Small changes to first paragraph --- docs/user_guide/examples/explanation_grids.md | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/docs/user_guide/examples/explanation_grids.md b/docs/user_guide/examples/explanation_grids.md index f6292631df..f8b487d9b8 100644 --- a/docs/user_guide/examples/explanation_grids.md +++ b/docs/user_guide/examples/explanation_grids.md @@ -1,6 +1,8 @@ # 📖 Grids -In Lagrangian ocean analysis, virtual particle tracking requires the accurate interpolation of physical properties (flow velocities and tracer properties) to particle locations. The underlying data that forces the particle movement will likely be defined on a discretised grid. Parcels can natively handle two styles of grids; structured and unstructured, where parcels `Field` objects exist on a (structured) `parcels.XGrid` or (unstructured) `parcels.Uxgrid`. Here we describe these grids on a conceptual level. +In Lagrangian ocean analysis, virtual particle tracking requires the accurate interpolation of physical properties (flow velocities and tracer properties) to particle locations. The underlying data that forces the particle movement will likely be defined on a discretised grid. Parcels can natively handle two styles of grids; structured and (triangular) unstructured, where parcels `Field` objects exist on a (structured) `parcels.XGrid` or (unstructured) `parcels.UxGrid`. Here we describe these grids on a conceptual level. + +Under the hood, every `Field` in a `FieldSet` has a `grid` attribute. This `grid` stores the spatial and temporal information of the Field coordinates. The number of Grids in a FieldSet is thus always smaller or equal to the number of Field objects; and this is what the "grid number" column in `FieldSet.describe()` refers to. ## Structured grids From 2b1c61f5d7be7900c8806c40efc1975a1bafd967 Mon Sep 17 00:00:00 2001 From: Erik van Sebille Date: Wed, 29 Jul 2026 17:36:51 +0200 Subject: [PATCH 06/17] Update explanation_grids.md --- docs/user_guide/examples/explanation_grids.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/user_guide/examples/explanation_grids.md b/docs/user_guide/examples/explanation_grids.md index f8b487d9b8..8251aff8e7 100644 --- a/docs/user_guide/examples/explanation_grids.md +++ b/docs/user_guide/examples/explanation_grids.md @@ -1,6 +1,6 @@ # 📖 Grids -In Lagrangian ocean analysis, virtual particle tracking requires the accurate interpolation of physical properties (flow velocities and tracer properties) to particle locations. The underlying data that forces the particle movement will likely be defined on a discretised grid. Parcels can natively handle two styles of grids; structured and (triangular) unstructured, where parcels `Field` objects exist on a (structured) `parcels.XGrid` or (unstructured) `parcels.UxGrid`. Here we describe these grids on a conceptual level. +In Lagrangian ocean analysis, virtual particle tracking requires the accurate interpolation of physical properties (flow velocities and tracer properties) to particle locations. The underlying data that forces the particle movement will likely be defined on a discretised grid. Parcels can natively handle two styles of horizontal grids; structured and (triangular) unstructured, where parcels `Field` objects exist on a (structured) `parcels.XGrid` or (unstructured) `parcels.UxGrid`. Here we describe these grids on a conceptual level. Under the hood, every `Field` in a `FieldSet` has a `grid` attribute. This `grid` stores the spatial and temporal information of the Field coordinates. The number of Grids in a FieldSet is thus always smaller or equal to the number of Field objects; and this is what the "grid number" column in `FieldSet.describe()` refers to. From 8ec6bca894db8905ef7cf132f5b7d3df418b0fbb Mon Sep 17 00:00:00 2001 From: Michael Denes Date: Fri, 31 Jul 2026 10:06:34 +0200 Subject: [PATCH 07/17] Adding code snippets and Erik's suggestions. Some to do's still to complete. --- docs/user_guide/examples/explanation_grids.md | 161 +++++++++++++++++- 1 file changed, 153 insertions(+), 8 deletions(-) diff --git a/docs/user_guide/examples/explanation_grids.md b/docs/user_guide/examples/explanation_grids.md index 8943a86112..6584e9f4bb 100644 --- a/docs/user_guide/examples/explanation_grids.md +++ b/docs/user_guide/examples/explanation_grids.md @@ -1,13 +1,17 @@ # 📖 Grids -In Lagrangian ocean analysis, virtual particle tracking requires the accurate interpolation of physical properties (flow velocities and tracer properties) to particle locations. The underlying data that forces the particle movement will likely be defined on a discretised grid. Parcels can natively handle two styles of grids; structured and unstructured, where parcels `Field` objects exist on a (structured) `parcels.XGrid` or (unstructured) `parcels.Uxgrid`. Here we describe these grids on a conceptual level. +In Lagrangian ocean analysis, virtual particle tracking requires the accurate interpolation of physical properties (flow velocities and tracer properties) to particle locations. The underlying data that forces the particle movement will likely be defined on a discretised grid. Parcels can natively handle two styles of grids; structured and unstructured, where parcels `Field` objects exist on a (structured) `parcels.XGrid` and conform to [SGRID](https://sgrid.github.io/sgrid/) conventions, or on a (unstructured) `parcels.Uxgrid` and conform to [UGRID](https://ugrid-conventions.github.io/ugrid-conventions/) conventions. Here we describe these grids on a conceptual level. ## Structured grids -A structured grid is composed of quadrilateral elements, that are indexed using logical 2D or 3D indices, like $(i,j,k)$. In `xarray` terminology, these indices correspond to `dimensions`, for example [...]. In structured grids, grid cell neighbours are easily found by decrementing or incrementing these dimensions. +A structured grid is composed of quadrilateral elements, that are indexed using logical 2D or 3D indices, like $(i,j,k)$. In `xarray` terminology, these indices correspond to `dimensions`, for example [...]. A major benefit of structured grids is that grid cell neighbours are easily found by decrementing or incrementing these dimensions. However, in parcels we either perform a binary search in the case of 1-dimensional coordinates, or use a hash table in the case of 2/3-dimensional coordinates. -There are two styles of structured grids, rectilinear and curvilinear, as shown in Figure 1. Rectilinear grids are nearly always aligned with the coordinate axes (that is, there is a one-to-one mapping between the dimensions and the physical coordinate space), making them simple and computationally efficient to query. However, they're limited by the fact that it is difficult to resolve complex coastlines without high resolution, and they suffer from singularities in the flow fields at the poles where the grid lines converge. Curvilinear grids allow for curved grid lines, which allow for better representation of coastlines. They often move the poles onto land to avoid singularities occuring in the ocean. However, they become trickier to work with, as the spatial positions of their vertices are stored in separate 2D arrays, and moving to an eastward neighbour is not as simple as incrementing the $i$-th coordinate by 1. +There are two styles of structured grids, rectilinear and curvilinear, as shown in Figure 1. -![Figure 1 from parcels v2 paper](image.png) +1. Rectilinear grids are typically aligned with the coordinate axes (that is, there is a one-to-one mapping between the dimensions and the physical coordinate space), making them simple and computationally efficient to query. However, they're limited by the fact that it is difficult to resolve complex coastlines without high resolution, and they suffer from singularities in the flow fields at the poles where the grid lines converge. + +2. Curvilinear grids allow for curved grid lines, which allow for better representation of coastlines. They often move the poles onto land to avoid singularities occuring in the ocean. However, they become trickier to work with, as the spatial positions of their vertices (their ["coordinates" in xarray-parlance](https://docs.xarray.dev/en/latest/user-guide/terminology.html#term-Coordinate)) are stored in separate 2D arrays, and moving to an eastward neighbour is not as simple as incrementing the $i$-th dimension by 1. + +![Figure 1 - Grid discretizations in the horizontal plane; (a) rectilinear, (b) curvilinear. Adapted from [Parcels v2.0 paper](https://doi.org/10.5194/gmd-12-3571-2019)](image.png) ## Unstructured grids @@ -18,18 +22,159 @@ TODO: For Joe. Regardless of your grid type, how your data is defined on your grid is equally important. Here, we will describe how you can interpret your data at a very general level, and the concept applies for any $n$-gon ($n$-sided polygon with $n \ge 3$). ### Nodes, edges, and faces -Let's assume we have a simple 2D rectlinear grid. The grid is composed of a number of nodes (or vertices), connected by edges, which together construct grid cells and grid cell faces. In Figure 2, we draw a simple grid cell. Here, your data may be defined on the corners of the grid cell (the nodes/vertices), at the centre of the cell face, or across a cell edge. +Let's assume we have a simple 2D rectilinear grid. The grid is composed of a number of nodes (or vertices), connected by edges, which together construct grid cells and grid cell faces. In Figure 2, we draw a simple grid cell. Here, your data may be defined on the corners of the grid cell (the nodes/vertices), at the centre of the cell face, or across a cell edge. ![Figure 2 - A simple grid cell. Blue circles denote nodes (or vertices) of the grid cell. The red circle denotes the centre of the cell face.](image-1.png) -You will need to make several assumptions about your data. Your data may represent a point-wise "sample" of some field. For example, velocity data may be defined at the nodes of your grid, and a fairly safe assumption to make is that you can bi-linearly interpolate these data points to your particle positions. In such an example, your velocity field may look like Figure 3. +You will need to make several assumptions about your data. Your data may represent a point-wise "sample" of some field. For example, velocity data may be defined at the nodes of your grid, and a typical assumption to make is that you can bi-linearly interpolate these data points to your particle positions. In such an example, your velocity field may look like Figure 3. + +

+Code to generate Figure 3 +```python +import numpy as np +import matplotlib.pyplot as plt +from scipy.interpolate import interp2d + +xx, yy = np.meshgrid(np.linspace(0,1,2), np.linspace(0,1,2), indexing='ij') +interp_xx, interp_yy = np.linspace(0,1,51), np.linspace(0,1,51) +u_data = np.array([[0, -0.5], [1, -1]]) +v_data = np.array([[0, -2], [0, -2]]) + +interp_u = interp2d(xx.flatten(), yy.flatten(), u_data.flatten(), kind='linear') +interp_u_data = interp_u(np.linspace(0,1,51), np.linspace(0,1,51)) + +interp_v = interp2d(xx.flatten(), yy.flatten(), v_data.flatten(), kind='linear') +interp_v_data = interp_v(np.linspace(0,1,51), np.linspace(0,1,51)) + +interp_speed_data = np.sqrt(interp_u_data**2 + interp_v_data**2) + +mm=5 +plt.axhline(0, linewidth=0.5, color='k') +plt.axvline(0, linewidth=0.5, color='k') +plt.axhline(1, linewidth=0.5, color='k') +plt.axvline(1, linewidth=0.5, color='k') +cb = plt.pcolormesh(interp_xx, interp_yy, interp_speed_data, shading='gouraud', cmap=plt.cm.viridis) +plt.quiver(interp_xx[::mm], interp_yy[::mm], interp_u_data[::mm,::mm], interp_v_data[::mm,::mm]) +plt.title("Bi-linear interpolation of velocity data at nodes") + +plt.colorbar(cb, ax=plt.gca(), label='Speed [m/s]') +plt.xlabel('X [km]') +plt.ylabel('Y [km]') + +plt.xlim([-0.2,1.2]) +plt.ylim([-0.2,1.2]) +``` +
![Figure 3 - Bi-linear interpolation of point-wise data at nodes](image-2.png) -Alternatively, your data may represent an "average value" across a cell face. For example, your temperature and salinity data may be defined at the cell centre, and represent an average value for the entire grid cell. A fairly safe assumption to make is that you can nearest-neighbour interpolate these data points to your particle positions. In such a case, your temperature field may look like figure 4. +Alternatively, your data may represent an "average value" across a cell face. For example, your temperature and salinity data may be defined at the cell centre, and represent an average value for the entire grid cell. A typical assumption to make is that you can nearest-neighbour interpolate these data points to your particle positions. In such a case, your temperature field may look like figure 4. + +
+Code to generate Figure 4 +```python +import numpy as np +import matplotlib.pyplot as plt + +xx, yy = np.meshgrid(np.linspace(0,1,2), np.linspace(0,1,2), indexing='ij') +data = np.array([[-1, 1], [0, 2]]) +mm=5 +for i in [1,-1]: + for j in [-1, 1]: + plt.pcolormesh(xx + i*0.5, yy + j*0.5, 18+np.random.rand(1)*data, shading='auto', cmap=plt.cm.viridis) + plt.scatter(xx+ i*0.5, yy + j*0.5, c='k', zorder=20) +cb = plt.pcolormesh(xx+0.5, yy + 0.5, 18 + 0.5*data, shading='auto', cmap=plt.cm.viridis, zorder=10) + +plt.title(f"Nearest-neighbour interpolation of\ntemperature data at cell centres") + +plt.colorbar(cb, ax=plt.gca(), label='Temperature [deg C]') +plt.xlabel('X [km]') +plt.ylabel('Y [km]') +plt.axhline(-1, linewidth=0.5, color='k', zorder=30) +plt.axhline(0, linewidth=0.5, color='k', zorder=30) +plt.axhline(1, linewidth=0.5, color='k', zorder=30) +plt.axhline(2, linewidth=0.5, color='k', zorder=30) +plt.axvline(-1, linewidth=0.5, color='k', zorder=30) +plt.axvline(0, linewidth=0.5, color='k', zorder=30) +plt.axvline(1, linewidth=0.5, color='k', zorder=30) +plt.axvline(2, linewidth=0.5, color='k', zorder=30) + +plt.xlim([-1,2]) +plt.ylim([-1,2]) +plt.show() +``` +
![Figure 4 - Nearest-neighbour interpolation of "grid cell averaged" data at cell centres](image-4.png) -Lastly, your data may represent a value across a cell edge. For example, in (2D) Arakawa C-grid datasets, velocities are defined across an edge as they represent a "flux" across that cell edge. [for some reason an accepted assumption is] to perform a 1D linear interpolation of the zonal velocity in the zonal direction, and similarly a 1D linear interpolation of the meridional velocity in the meridional direction. In such a case, your velocity field may look like figure 5. +Your data may represent a value across a cell edge. For example, in (2D) Arakawa C-grid datasets, velocities are defined across an edge as they represent a "flux" across that cell edge. Additionally, these cell edges may not be aligned with the coordinate axes, and rather represent a velocity in the $i$ or $j$ direction. For structured grids, [Blanke and Raynaud](https://doi.org/10.1175/1520-0485(1997)027%3C1038:KOTPEU%3E2.0.CO;2) proposed in 1997 to perform a 1D linear interpolation of the $i$ velocity in the $i$ direction, and similarly a 1D linear interpolation of the $j$ velocity in the $j$ direction. These velocities must then be rotated into meridional and zonal velocities, which parcels handles under the hood. In such a case, your velocity field may look like figure 5. +This (uni)linear velocity interpolation is now often referred to as the Analytical interpolation scheme, and is what the [Ariane](https://ariane-code.cnrs.fr) and [TRACMASS](https://www.tracmass.org/index.html) Lagrangian codes also use. In Parcels, the time-stepping version of this interpolation is provided in the `CGrid_Velocity` Interpolator function. + +
+Code to generate Figure 5 +```python +import numpy as np +import matplotlib.pyplot as plt +from scipy.interpolate import interp1d + +interp_xx, interp_yy = np.linspace(0,1,51), np.linspace(0,1,51) +XX,YY = np.meshgrid(interp_xx, interp_yy, indexing='xy') +u_data = np.array([[2, 1]]) +v_data = np.array([[0, 1]]) + +interp_u = interp1d([0,1], u_data.flatten(), kind='linear') +interp_v = interp1d([0,1], v_data.flatten(), kind='linear') + +interp_u_data = interp_u(XX) +interp_v_data = interp_v(YY) +interp_speed_data = np.sqrt(interp_u_data**2 + interp_v_data**2) + +mm=5 +plt.axhline(0, linewidth=0.5, color='k') +plt.axvline(0, linewidth=0.5, color='k') +plt.axhline(1, linewidth=0.5, color='k') +plt.axvline(1, linewidth=0.5, color='k') +cb = plt.pcolormesh(interp_xx, interp_yy, interp_speed_data, vmin=0.75, vmax=2) +plt.quiver(interp_xx[::mm], interp_yy[::mm], interp_u_data[::mm,::mm], interp_v_data[::mm,::mm]) +plt.title(f"C-grid interpolation of velocity data\nacross cell edges") +plt.quiver(interp_xx[0], interp_yy[len(interp_yy)//2], + interp_u_data[len(interp_u_data)//2, 0], + 0, + color='r', + scale=30) +plt.quiver(interp_xx[-1], interp_yy[len(interp_yy)//2], + interp_u_data[len(interp_u_data)//2, -1], + 0, + color='r', + scale=30) + +plt.quiver(interp_xx[len(interp_yy)//2], interp_yy[0], + 0, + interp_v_data[0, len(interp_v_data)//2], + color='b') +plt.quiver(interp_xx[len(interp_yy)//2], interp_yy[-1], + 0, + interp_v_data[-1, len(interp_v_data)//2], + color='b') + +plt.colorbar(cb, ax=plt.gca(), label='Speed [m/s]') +plt.xlim([-0.2,1.2]) +plt.ylim([-0.2,1.2]) +plt.xlabel('X [km]') +plt.ylabel('Y [km]') +plt.show() +``` +
![Figure 5 - C-grid 1D interpolation of velocity data defined across a cell edge](image-5.png) + + +### Vertical coordinates + +Lastly, a short note on vertical coordinates. Parcels can handle two styles of vertical coordinates; z-levels which define fixed depth levels in physical space, and sigma-levels which define varying depth levels in physical space as a function of the water column depth. As sigma-levels are effectively "terrain-following", the grid cell faces may no longer be orthogonal to the domain surface. Figure 1 visualises these differences, and parcels handles this all under the hood. See the CROCO Tutorial for more details on the sigma-levels implementation. + + +### TODO: Add note on convert functions +- support for many common ocean model outputs -> converts xarray datasets into SGRID/UGRID compliant datasets. +- if your model is not currently supported, you can write your own, or reach out by raising a discussion thread. +- your grid determines the type of interpolater you will use. \ No newline at end of file From 5de7811f29778f1d56f1abd7d320c77f9743fb1b Mon Sep 17 00:00:00 2001 From: Michael Denes Date: Fri, 31 Jul 2026 10:16:08 +0200 Subject: [PATCH 08/17] Re-adding parts that were missed when resolving the merge conflicts. --- docs/user_guide/examples/explanation_grids.md | 14 ++++++-------- 1 file changed, 6 insertions(+), 8 deletions(-) diff --git a/docs/user_guide/examples/explanation_grids.md b/docs/user_guide/examples/explanation_grids.md index a1f4d2d046..1f9a4d8b86 100644 --- a/docs/user_guide/examples/explanation_grids.md +++ b/docs/user_guide/examples/explanation_grids.md @@ -1,12 +1,11 @@ # 📖 Grids -In Lagrangian ocean analysis, virtual particle tracking requires the accurate interpolation of physical properties (flow velocities and tracer properties) to particle locations. The underlying data that forces the particle movement will likely be defined on a discretised grid. Parcels can natively handle two styles of horizontal grids; structured and (triangular) unstructured, where parcels `Field` objects exist on a (structured) `parcels.XGrid` or (unstructured) `parcels.UxGrid`. Here we describe these grids on a conceptual level. +In Lagrangian ocean analysis, virtual particle tracking requires the accurate interpolation of physical properties (flow velocities and tracer properties) to particle locations. The underlying data that forces the particle movement will likely be defined on a discretised grid. Parcels can natively handle two styles of grids; structured and unstructured, where parcels `Field` objects exist on a (structured) `parcels.XGrid` and conform to [SGRID](https://sgrid.github.io/sgrid/) conventions, or on a (unstructured) `parcels.Uxgrid` and conform to [UGRID](https://ugrid-conventions.github.io/ugrid-conventions/) conventions. Here we describe these grids on a conceptual level. Under the hood, every `Field` in a `FieldSet` has a `grid` attribute. This `grid` stores the spatial and temporal information of the Field coordinates. The number of Grids in a FieldSet is thus always smaller or equal to the number of Field objects; and this is what the "grid number" column in `FieldSet.describe()` refers to. ## Structured grids - -A structured grid is composed of quadrilateral elements, that are indexed using logical 2D or 3D indices, like $(i,j,k)$. In `xarray` terminology, these indices correspond to `dimensions`, for example [...]. In structured grids, grid cell neighbours are easily found by decrementing or incrementing these dimensions. +A structured grid is composed of quadrilateral elements, that are indexed using logical 2D or 3D indices, like $(i,j,k)$. In `xarray` terminology, these indices correspond to `dimensions`, for example [...]. A major benefit of structured grids is that grid cell neighbours are easily found by decrementing or incrementing these dimensions. However, in parcels we either perform a binary search in the case of 1-dimensional coordinates, or use a hash table in the case of 2/3-dimensional coordinates. There are two styles of structured grids, rectilinear and curvilinear, as shown in Figure 1. @@ -16,17 +15,16 @@ There are two styles of structured grids, rectilinear and curvilinear, as shown ![Figure 1 - Grid discretizations in the horizontal plane; (a) rectilinear, (b) curvilinear. Adapted from [Parcels v2.0 paper](https://doi.org/10.5194/gmd-12-3571-2019)](image.png) -## Unstructured grids +## Unstructured grids TODO: For Joe. -## How your data may be defined +## How your data may be defined Regardless of your grid type, how your data is defined on your grid is equally important. Here, we will describe how you can interpret your data at a very general level, and the concept applies for any $n$-gon ($n$-sided polygon with $n \ge 3$). ### Nodes, edges, and faces - -Let's assume we have a simple 2D rectlinear grid. The grid is composed of a number of nodes (or vertices), connected by edges, which together construct grid cells and grid cell faces. In Figure 2, we draw a simple grid cell. Here, your data may be defined on the corners of the grid cell (the nodes/vertices), at the centre of the cell face, or across a cell edge. +Let's assume we have a simple 2D rectilinear grid. The grid is composed of a number of nodes (or vertices), connected by edges, which together construct grid cells and grid cell faces. In Figure 2, we draw a simple grid cell. Here, your data may be defined on the corners of the grid cell (the nodes/vertices), at the centre of the cell face, or across a cell edge. ![Figure 2 - A simple grid cell. Blue circles denote nodes (or vertices) of the grid cell. The red circle denotes the centre of the cell face.](image-1.png) @@ -181,4 +179,4 @@ Lastly, a short note on vertical coordinates. Parcels can handle two styles of v ### TODO: Add note on convert functions - support for many common ocean model outputs -> converts xarray datasets into SGRID/UGRID compliant datasets. - if your model is not currently supported, you can write your own, or reach out by raising a discussion thread. -- your grid determines the type of interpolater you will use. \ No newline at end of file +- your grid determines the type of interpolater you will use. From b4a4f5ec0ef0fa644c673875059c6d1306a433e1 Mon Sep 17 00:00:00 2001 From: "pre-commit-ci[bot]" <66853113+pre-commit-ci[bot]@users.noreply.github.com> Date: Fri, 31 Jul 2026 08:16:20 +0000 Subject: [PATCH 09/17] [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci --- docs/user_guide/examples/explanation_grids.md | 58 ++++++++++--------- 1 file changed, 32 insertions(+), 26 deletions(-) diff --git a/docs/user_guide/examples/explanation_grids.md b/docs/user_guide/examples/explanation_grids.md index 1f9a4d8b86..ababdc6a50 100644 --- a/docs/user_guide/examples/explanation_grids.md +++ b/docs/user_guide/examples/explanation_grids.md @@ -5,6 +5,7 @@ In Lagrangian ocean analysis, virtual particle tracking requires the accurate in Under the hood, every `Field` in a `FieldSet` has a `grid` attribute. This `grid` stores the spatial and temporal information of the Field coordinates. The number of Grids in a FieldSet is thus always smaller or equal to the number of Field objects; and this is what the "grid number" column in `FieldSet.describe()` refers to. ## Structured grids + A structured grid is composed of quadrilateral elements, that are indexed using logical 2D or 3D indices, like $(i,j,k)$. In `xarray` terminology, these indices correspond to `dimensions`, for example [...]. A major benefit of structured grids is that grid cell neighbours are easily found by decrementing or incrementing these dimensions. However, in parcels we either perform a binary search in the case of 1-dimensional coordinates, or use a hash table in the case of 2/3-dimensional coordinates. There are two styles of structured grids, rectilinear and curvilinear, as shown in Figure 1. @@ -15,15 +16,16 @@ There are two styles of structured grids, rectilinear and curvilinear, as shown ![Figure 1 - Grid discretizations in the horizontal plane; (a) rectilinear, (b) curvilinear. Adapted from [Parcels v2.0 paper](https://doi.org/10.5194/gmd-12-3571-2019)](image.png) - ## Unstructured grids -TODO: For Joe. +TODO: For Joe. ## How your data may be defined + Regardless of your grid type, how your data is defined on your grid is equally important. Here, we will describe how you can interpret your data at a very general level, and the concept applies for any $n$-gon ($n$-sided polygon with $n \ge 3$). ### Nodes, edges, and faces + Let's assume we have a simple 2D rectilinear grid. The grid is composed of a number of nodes (or vertices), connected by edges, which together construct grid cells and grid cell faces. In Figure 2, we draw a simple grid cell. Here, your data may be defined on the corners of the grid cell (the nodes/vertices), at the centre of the cell face, or across a cell edge. ![Figure 2 - A simple grid cell. Blue circles denote nodes (or vertices) of the grid cell. The red circle denotes the centre of the cell face.](image-1.png) @@ -51,9 +53,9 @@ interp_v_data = interp_v(np.linspace(0,1,51), np.linspace(0,1,51)) interp_speed_data = np.sqrt(interp_u_data**2 + interp_v_data**2) mm=5 -plt.axhline(0, linewidth=0.5, color='k') +plt.axhline(0, linewidth=0.5, color='k') plt.axvline(0, linewidth=0.5, color='k') -plt.axhline(1, linewidth=0.5, color='k') +plt.axhline(1, linewidth=0.5, color='k') plt.axvline(1, linewidth=0.5, color='k') cb = plt.pcolormesh(interp_xx, interp_yy, interp_speed_data, shading='gouraud', cmap=plt.cm.viridis) plt.quiver(interp_xx[::mm], interp_yy[::mm], interp_u_data[::mm,::mm], interp_v_data[::mm,::mm]) @@ -65,7 +67,8 @@ plt.ylabel('Y [km]') plt.xlim([-0.2,1.2]) plt.ylim([-0.2,1.2]) -``` + +```` ![Figure 3 - Bi-linear interpolation of point-wise data at nodes](image-2.png) @@ -93,10 +96,10 @@ plt.colorbar(cb, ax=plt.gca(), label='Temperature [deg C]') plt.xlabel('X [km]') plt.ylabel('Y [km]') plt.axhline(-1, linewidth=0.5, color='k', zorder=30) -plt.axhline(0, linewidth=0.5, color='k', zorder=30) +plt.axhline(0, linewidth=0.5, color='k', zorder=30) plt.axhline(1, linewidth=0.5, color='k', zorder=30) plt.axhline(2, linewidth=0.5, color='k', zorder=30) -plt.axvline(-1, linewidth=0.5, color='k', zorder=30) +plt.axvline(-1, linewidth=0.5, color='k', zorder=30) plt.axvline(0, linewidth=0.5, color='k', zorder=30) plt.axvline(1, linewidth=0.5, color='k', zorder=30) plt.axvline(2, linewidth=0.5, color='k', zorder=30) @@ -104,12 +107,13 @@ plt.axvline(2, linewidth=0.5, color='k', zorder=30) plt.xlim([-1,2]) plt.ylim([-1,2]) plt.show() -``` +```` + ![Figure 4 - Nearest-neighbour interpolation of "grid cell averaged" data at cell centres](image-4.png) -Your data may represent a value across a cell edge. For example, in (2D) Arakawa C-grid datasets, velocities are defined across an edge as they represent a "flux" across that cell edge. Additionally, these cell edges may not be aligned with the coordinate axes, and rather represent a velocity in the $i$ or $j$ direction. For structured grids, [Blanke and Raynaud](https://doi.org/10.1175/1520-0485(1997)027%3C1038:KOTPEU%3E2.0.CO;2) proposed in 1997 to perform a 1D linear interpolation of the $i$ velocity in the $i$ direction, and similarly a 1D linear interpolation of the $j$ velocity in the $j$ direction. These velocities must then be rotated into meridional and zonal velocities, which parcels handles under the hood. In such a case, your velocity field may look like figure 5. +Your data may represent a value across a cell edge. For example, in (2D) Arakawa C-grid datasets, velocities are defined across an edge as they represent a "flux" across that cell edge. Additionally, these cell edges may not be aligned with the coordinate axes, and rather represent a velocity in the $i$ or $j$ direction. For structured grids, [Blanke and Raynaud]() proposed in 1997 to perform a 1D linear interpolation of the $i$ velocity in the $i$ direction, and similarly a 1D linear interpolation of the $j$ velocity in the $j$ direction. These velocities must then be rotated into meridional and zonal velocities, which parcels handles under the hood. In such a case, your velocity field may look like figure 5. This (uni)linear velocity interpolation is now often referred to as the Analytical interpolation scheme, and is what the [Ariane](https://ariane-code.cnrs.fr) and [TRACMASS](https://www.tracmass.org/index.html) Lagrangian codes also use. In Parcels, the time-stepping version of this interpolation is provided in the `CGrid_Velocity` Interpolator function.
@@ -119,7 +123,7 @@ import numpy as np import matplotlib.pyplot as plt from scipy.interpolate import interp1d -interp_xx, interp_yy = np.linspace(0,1,51), np.linspace(0,1,51) +interp_xx, interp_yy = np.linspace(0,1,51), np.linspace(0,1,51) XX,YY = np.meshgrid(interp_xx, interp_yy, indexing='xy') u_data = np.array([[2, 1]]) v_data = np.array([[0, 1]]) @@ -132,32 +136,32 @@ interp_v_data = interp_v(YY) interp_speed_data = np.sqrt(interp_u_data**2 + interp_v_data**2) mm=5 -plt.axhline(0, linewidth=0.5, color='k') +plt.axhline(0, linewidth=0.5, color='k') plt.axvline(0, linewidth=0.5, color='k') -plt.axhline(1, linewidth=0.5, color='k') +plt.axhline(1, linewidth=0.5, color='k') plt.axvline(1, linewidth=0.5, color='k') cb = plt.pcolormesh(interp_xx, interp_yy, interp_speed_data, vmin=0.75, vmax=2) plt.quiver(interp_xx[::mm], interp_yy[::mm], interp_u_data[::mm,::mm], interp_v_data[::mm,::mm]) plt.title(f"C-grid interpolation of velocity data\nacross cell edges") plt.quiver(interp_xx[0], interp_yy[len(interp_yy)//2], - interp_u_data[len(interp_u_data)//2, 0], - 0, - color='r', - scale=30) +interp_u_data[len(interp_u_data)//2, 0], +0, +color='r', +scale=30) plt.quiver(interp_xx[-1], interp_yy[len(interp_yy)//2], - interp_u_data[len(interp_u_data)//2, -1], - 0, - color='r', - scale=30) +interp_u_data[len(interp_u_data)//2, -1], +0, +color='r', +scale=30) plt.quiver(interp_xx[len(interp_yy)//2], interp_yy[0], - 0, - interp_v_data[0, len(interp_v_data)//2], - color='b') +0, +interp_v_data[0, len(interp_v_data)//2], +color='b') plt.quiver(interp_xx[len(interp_yy)//2], interp_yy[-1], - 0, - interp_v_data[-1, len(interp_v_data)//2], - color='b') +0, +interp_v_data[-1, len(interp_v_data)//2], +color='b') plt.colorbar(cb, ax=plt.gca(), label='Speed [m/s]') plt.xlim([-0.2,1.2]) @@ -165,6 +169,7 @@ plt.ylim([-0.2,1.2]) plt.xlabel('X [km]') plt.ylabel('Y [km]') plt.show() + ```
@@ -180,3 +185,4 @@ Lastly, a short note on vertical coordinates. Parcels can handle two styles of v - support for many common ocean model outputs -> converts xarray datasets into SGRID/UGRID compliant datasets. - if your model is not currently supported, you can write your own, or reach out by raising a discussion thread. - your grid determines the type of interpolater you will use. +``` From 27999bdb18e33ae20a1f36a8d633fc7cdc6988da Mon Sep 17 00:00:00 2001 From: Michael Denes Date: Fri, 31 Jul 2026 10:21:51 +0200 Subject: [PATCH 10/17] Too many quote marks --- docs/user_guide/examples/explanation_grids.md | 7 +++---- 1 file changed, 3 insertions(+), 4 deletions(-) diff --git a/docs/user_guide/examples/explanation_grids.md b/docs/user_guide/examples/explanation_grids.md index ababdc6a50..08cb7ab53f 100644 --- a/docs/user_guide/examples/explanation_grids.md +++ b/docs/user_guide/examples/explanation_grids.md @@ -68,7 +68,7 @@ plt.ylabel('Y [km]') plt.xlim([-0.2,1.2]) plt.ylim([-0.2,1.2]) -```` +``` ![Figure 3 - Bi-linear interpolation of point-wise data at nodes](image-2.png) @@ -107,7 +107,7 @@ plt.axvline(2, linewidth=0.5, color='k', zorder=30) plt.xlim([-1,2]) plt.ylim([-1,2]) plt.show() -```` +``` @@ -184,5 +184,4 @@ Lastly, a short note on vertical coordinates. Parcels can handle two styles of v ### TODO: Add note on convert functions - support for many common ocean model outputs -> converts xarray datasets into SGRID/UGRID compliant datasets. - if your model is not currently supported, you can write your own, or reach out by raising a discussion thread. -- your grid determines the type of interpolater you will use. -``` +- your grid determines the type of interpolater you will use. \ No newline at end of file From 524d8f676fc83269edf7529a6c4e3381ada8aa64 Mon Sep 17 00:00:00 2001 From: "pre-commit-ci[bot]" <66853113+pre-commit-ci[bot]@users.noreply.github.com> Date: Fri, 31 Jul 2026 08:22:02 +0000 Subject: [PATCH 11/17] [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci --- docs/user_guide/examples/explanation_grids.md | 7 ++++--- 1 file changed, 4 insertions(+), 3 deletions(-) diff --git a/docs/user_guide/examples/explanation_grids.md b/docs/user_guide/examples/explanation_grids.md index 08cb7ab53f..ababdc6a50 100644 --- a/docs/user_guide/examples/explanation_grids.md +++ b/docs/user_guide/examples/explanation_grids.md @@ -68,7 +68,7 @@ plt.ylabel('Y [km]') plt.xlim([-0.2,1.2]) plt.ylim([-0.2,1.2]) -``` +```` ![Figure 3 - Bi-linear interpolation of point-wise data at nodes](image-2.png) @@ -107,7 +107,7 @@ plt.axvline(2, linewidth=0.5, color='k', zorder=30) plt.xlim([-1,2]) plt.ylim([-1,2]) plt.show() -``` +```` @@ -184,4 +184,5 @@ Lastly, a short note on vertical coordinates. Parcels can handle two styles of v ### TODO: Add note on convert functions - support for many common ocean model outputs -> converts xarray datasets into SGRID/UGRID compliant datasets. - if your model is not currently supported, you can write your own, or reach out by raising a discussion thread. -- your grid determines the type of interpolater you will use. \ No newline at end of file +- your grid determines the type of interpolater you will use. +``` From ce464aafdc7f8fd0af290a45ebb3826f6e9651cc Mon Sep 17 00:00:00 2001 From: Michael Denes Date: Fri, 31 Jul 2026 10:27:01 +0200 Subject: [PATCH 12/17] Updating figure to include vertical plane, and the caption. --- docs/user_guide/examples/explanation_grids.md | 2 +- docs/user_guide/examples/image.png | Bin 95840 -> 104523 bytes 2 files changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/user_guide/examples/explanation_grids.md b/docs/user_guide/examples/explanation_grids.md index ababdc6a50..356d641d1f 100644 --- a/docs/user_guide/examples/explanation_grids.md +++ b/docs/user_guide/examples/explanation_grids.md @@ -14,7 +14,7 @@ There are two styles of structured grids, rectilinear and curvilinear, as shown 2. Curvilinear grids allow for curved grid lines, which allow for better representation of coastlines. They often move the poles onto land to avoid singularities occuring in the ocean. However, they become trickier to work with, as the spatial positions of their vertices (their ["coordinates" in xarray-parlance](https://docs.xarray.dev/en/latest/user-guide/terminology.html#term-Coordinate)) are stored in separate 2D arrays, and moving to an eastward neighbour is not as simple as incrementing the $i$-th dimension by 1. -![Figure 1 - Grid discretizations in the horizontal plane; (a) rectilinear, (b) curvilinear. Adapted from [Parcels v2.0 paper](https://doi.org/10.5194/gmd-12-3571-2019)](image.png) +![Figure 1 - Grid discretizations handled by Parcels. In the horizontal plane; (a) rectilinear, (b) curvilinear. In the vertical plane; (c) z-levels, (d) sigma-levels. 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zRcjqI1C-JzwUwk}SJ50SUq4Nbs)BMU8PpgqAykk2A2~i?R0MBA?f8&>$u*c2BaIFo zIj32KqH~%*z^pJ`8d`dC1wZVH$$y}h9OeXR3G$7Dap!&Uw>qmi5F?2kjROS1R1_aq zC%D6po*bgqt26M+fH0~ND*p!!*#dww7HOq3S%XP@e^`tezTlPuPjsoQ+(W}qLr;xX zBb>m11r5DVw*>XBKoHgF{#uIJTM*&aMN)9JA5l)gg0+QVQ zAr2?yDbsJDrfVRbJ-&>MxDCa@*T8W<+B;r16Tz(T=!62|96>l7pOP=)3<=2|MmHCU z9+SND6Nt;2@EdFWO^TbY55#}oLg&}KiZ*DdImjW+?AG-cK!rD>1%vq((H>F+4g*`i z^1FB~6Y=^=O%N1JJd*C070K<(W9x$l#usIu>Hv!4tvrA)YG8=^G1clY+DkP0PQ|z8 zpvlT?97wxC$J}mb-`nupDIwq{br@P2NL6Z!{2&kq@TzAG+z^{}Egu5lDJfG^g>$e*E8` z|M#0vQU31?{dW%`ChWgEVcUBA*CzaTC;YiRh~lfisl+mO=vvO1cT&NBdOAkhWt!(B F{s$Bln8^SD From 7f7ebc7f723e3ef9a5af15d79987b4a16bbcdb1b Mon Sep 17 00:00:00 2001 From: Michael Denes Date: Fri, 31 Jul 2026 10:35:25 +0200 Subject: [PATCH 13/17] Something again to do with the tick marks. --- docs/user_guide/examples/explanation_grids.md | 8 +++----- 1 file changed, 3 insertions(+), 5 deletions(-) diff --git a/docs/user_guide/examples/explanation_grids.md b/docs/user_guide/examples/explanation_grids.md index 356d641d1f..9a487c2a19 100644 --- a/docs/user_guide/examples/explanation_grids.md +++ b/docs/user_guide/examples/explanation_grids.md @@ -67,8 +67,8 @@ plt.ylabel('Y [km]') plt.xlim([-0.2,1.2]) plt.ylim([-0.2,1.2]) +``` -```` ![Figure 3 - Bi-linear interpolation of point-wise data at nodes](image-2.png) @@ -107,7 +107,7 @@ plt.axvline(2, linewidth=0.5, color='k', zorder=30) plt.xlim([-1,2]) plt.ylim([-1,2]) plt.show() -```` +``` @@ -169,7 +169,6 @@ plt.ylim([-0.2,1.2]) plt.xlabel('X [km]') plt.ylabel('Y [km]') plt.show() - ``` @@ -184,5 +183,4 @@ Lastly, a short note on vertical coordinates. Parcels can handle two styles of v ### TODO: Add note on convert functions - support for many common ocean model outputs -> converts xarray datasets into SGRID/UGRID compliant datasets. - if your model is not currently supported, you can write your own, or reach out by raising a discussion thread. -- your grid determines the type of interpolater you will use. -``` +- your grid determines the type of interpolater you will use. \ No newline at end of file From 77ff473cb0f1911e9cab8adeccaeaaf51b2e95c0 Mon Sep 17 00:00:00 2001 From: "pre-commit-ci[bot]" <66853113+pre-commit-ci[bot]@users.noreply.github.com> Date: Fri, 31 Jul 2026 08:35:36 +0000 Subject: [PATCH 14/17] [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci --- docs/user_guide/examples/explanation_grids.md | 9 ++++++--- 1 file changed, 6 insertions(+), 3 deletions(-) diff --git a/docs/user_guide/examples/explanation_grids.md b/docs/user_guide/examples/explanation_grids.md index 9a487c2a19..f76d3e4448 100644 --- a/docs/user_guide/examples/explanation_grids.md +++ b/docs/user_guide/examples/explanation_grids.md @@ -67,7 +67,8 @@ plt.ylabel('Y [km]') plt.xlim([-0.2,1.2]) plt.ylim([-0.2,1.2]) -``` + +```` @@ -107,7 +108,7 @@ plt.axvline(2, linewidth=0.5, color='k', zorder=30) plt.xlim([-1,2]) plt.ylim([-1,2]) plt.show() -``` +```` @@ -169,6 +170,7 @@ plt.ylim([-0.2,1.2]) plt.xlabel('X [km]') plt.ylabel('Y [km]') plt.show() + ``` @@ -183,4 +185,5 @@ Lastly, a short note on vertical coordinates. Parcels can handle two styles of v ### TODO: Add note on convert functions - support for many common ocean model outputs -> converts xarray datasets into SGRID/UGRID compliant datasets. - if your model is not currently supported, you can write your own, or reach out by raising a discussion thread. -- your grid determines the type of interpolater you will use. \ No newline at end of file +- your grid determines the type of interpolater you will use. +``` From ebecd3f28f9caf13ae30f541e30b2a0b50a5a3bb Mon Sep 17 00:00:00 2001 From: Michael Denes Date: Fri, 31 Jul 2026 11:18:29 +0200 Subject: [PATCH 15/17] Small note on dimensions and coordinates. --- docs/user_guide/examples/explanation_grids.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/user_guide/examples/explanation_grids.md b/docs/user_guide/examples/explanation_grids.md index f76d3e4448..2e94f97685 100644 --- a/docs/user_guide/examples/explanation_grids.md +++ b/docs/user_guide/examples/explanation_grids.md @@ -6,7 +6,7 @@ Under the hood, every `Field` in a `FieldSet` has a `grid` attribute. This `grid ## Structured grids -A structured grid is composed of quadrilateral elements, that are indexed using logical 2D or 3D indices, like $(i,j,k)$. In `xarray` terminology, these indices correspond to `dimensions`, for example [...]. A major benefit of structured grids is that grid cell neighbours are easily found by decrementing or incrementing these dimensions. However, in parcels we either perform a binary search in the case of 1-dimensional coordinates, or use a hash table in the case of 2/3-dimensional coordinates. +A structured grid is composed of quadrilateral elements, that are indexed using logical 2D or 3D indices, like $(i,j,k)$. In `xarray` terminology, these indices correspond to `dimensions`. For example, in NEMO datasets, $(x,y)$ typically define these dimensions horizontally, where the physical coordinates are $(glamf, gphif)$. A major benefit of structured grids is that grid cell neighbours are easily found by decrementing or incrementing these dimensions. However, in parcels we either perform a binary search in the case of 1-dimensional coordinates, or use a hash table in the case of 2/3-dimensional coordinates. There are two styles of structured grids, rectilinear and curvilinear, as shown in Figure 1. From 7dd6c701e427fe5b7934077a4ff770ec7947bc08 Mon Sep 17 00:00:00 2001 From: Michael Denes Date: Fri, 31 Jul 2026 11:39:51 +0200 Subject: [PATCH 16/17] Additional info on continuity and smoothness --- docs/user_guide/examples/explanation_grids.md | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/docs/user_guide/examples/explanation_grids.md b/docs/user_guide/examples/explanation_grids.md index 2e94f97685..7b55b582dc 100644 --- a/docs/user_guide/examples/explanation_grids.md +++ b/docs/user_guide/examples/explanation_grids.md @@ -30,7 +30,7 @@ Let's assume we have a simple 2D rectilinear grid. The grid is composed of a num ![Figure 2 - A simple grid cell. Blue circles denote nodes (or vertices) of the grid cell. The red circle denotes the centre of the cell face.](image-1.png) -You will need to make several assumptions about your data. Your data may represent a point-wise "sample" of some field. For example, velocity data may be defined at the nodes of your grid, and a typical assumption to make is that you can bi-linearly interpolate these data points to your particle positions. In such an example, your velocity field may look like Figure 3. +You will need to make several assumptions about your data. Your data may represent a point-wise "sample" of some field. For example, velocity data may be defined at the nodes of your grid, and a typical assumption to make is that you can bi-linearly interpolate these data points to your particle positions. In such an example, your velocity field may look like Figure 3. Bi-linear interpolation ensures continuity of the velocity at the cell boundaries, however, it does not ensure a smooth transition.
Code to generate Figure 3 @@ -74,7 +74,7 @@ plt.ylim([-0.2,1.2]) ![Figure 3 - Bi-linear interpolation of point-wise data at nodes](image-2.png) -Alternatively, your data may represent an "average value" across a cell face. For example, your temperature and salinity data may be defined at the cell centre, and represent an average value for the entire grid cell. A typical assumption to make is that you can nearest-neighbour interpolate these data points to your particle positions. In such a case, your temperature field may look like figure 4. +Alternatively, your data may represent an "average value" across a cell face. For example, your temperature and salinity data may be defined at the cell centre, and represent an average value for the entire grid cell. A typical assumption to make is that you can nearest-neighbour interpolate these data points to your particle positions. In such a case, your temperature field may look like figure 4. A nearest-neighbour interpolation scheme ensures you have a piece-wise constant field, typically with sharp transitions at grid cell boundaries.
Code to generate Figure 4 @@ -115,6 +115,7 @@ plt.show() ![Figure 4 - Nearest-neighbour interpolation of "grid cell averaged" data at cell centres](image-4.png) Your data may represent a value across a cell edge. For example, in (2D) Arakawa C-grid datasets, velocities are defined across an edge as they represent a "flux" across that cell edge. Additionally, these cell edges may not be aligned with the coordinate axes, and rather represent a velocity in the $i$ or $j$ direction. For structured grids, [Blanke and Raynaud]() proposed in 1997 to perform a 1D linear interpolation of the $i$ velocity in the $i$ direction, and similarly a 1D linear interpolation of the $j$ velocity in the $j$ direction. These velocities must then be rotated into meridional and zonal velocities, which parcels handles under the hood. In such a case, your velocity field may look like figure 5. + This (uni)linear velocity interpolation is now often referred to as the Analytical interpolation scheme, and is what the [Ariane](https://ariane-code.cnrs.fr) and [TRACMASS](https://www.tracmass.org/index.html) Lagrangian codes also use. In Parcels, the time-stepping version of this interpolation is provided in the `CGrid_Velocity` Interpolator function.
From 54ff5ecd514c7d88129db21f08bc69211872176a Mon Sep 17 00:00:00 2001 From: "pre-commit-ci[bot]" <66853113+pre-commit-ci[bot]@users.noreply.github.com> Date: Fri, 31 Jul 2026 09:40:04 +0000 Subject: [PATCH 17/17] [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci --- docs/user_guide/examples/explanation_grids.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/user_guide/examples/explanation_grids.md b/docs/user_guide/examples/explanation_grids.md index 7b55b582dc..0c54eaaba8 100644 --- a/docs/user_guide/examples/explanation_grids.md +++ b/docs/user_guide/examples/explanation_grids.md @@ -30,7 +30,7 @@ Let's assume we have a simple 2D rectilinear grid. The grid is composed of a num ![Figure 2 - A simple grid cell. Blue circles denote nodes (or vertices) of the grid cell. The red circle denotes the centre of the cell face.](image-1.png) -You will need to make several assumptions about your data. Your data may represent a point-wise "sample" of some field. For example, velocity data may be defined at the nodes of your grid, and a typical assumption to make is that you can bi-linearly interpolate these data points to your particle positions. In such an example, your velocity field may look like Figure 3. Bi-linear interpolation ensures continuity of the velocity at the cell boundaries, however, it does not ensure a smooth transition. +You will need to make several assumptions about your data. Your data may represent a point-wise "sample" of some field. For example, velocity data may be defined at the nodes of your grid, and a typical assumption to make is that you can bi-linearly interpolate these data points to your particle positions. In such an example, your velocity field may look like Figure 3. Bi-linear interpolation ensures continuity of the velocity at the cell boundaries, however, it does not ensure a smooth transition.
Code to generate Figure 3

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