HoloViz Visualization


The ability to dynamically render, pan, zoom, animate and perform other dynamic operations on data can provide many benefits, such as providing greater data fidelity within the same plot. HoloViz provides high-level tools (such as Holoviews, Datashader, Geoviews, etc.) to visualize even the very large datasets efficiently.

This notebook explores interactively plotting using an unstructured grid dataset in the MPAS format with Holoviews, Datashader, and Geoviews.


If you are in this notebook to actually learn about and/or visualize unstructured grids, we highly recommend checking out the UXarray Cookbook that is a comprehensive showcase of workflows & techniques for visualizing Unstructured Grids using UXarray. UXarray is a Python package that:

  • Provides Xarray-styled functionality for working with unstructured grids built around the UGRID conventions

  • Supports not only MPAS but also several other formats such as UGRID, SCRIP, and Exodus

  • Enables significant data analysis and visualization functionality for unstructured grid research, which makes working with unstructured grids a breeze

    • e.g. UXarray internally handles majority of the utility functions and data preparation steps mentioned throughout this notebook and provides user with convenient visualization and analysis functions

This notebook demonstrates:

  1. Use of HoloViz tools for interactive plotting

  2. Different interactivity schemes

  3. Use of the MPAS format’s connectivity information to render data on the native grid (hence avoiding costly Delaunay triangulation)

The flow of the content is as follows:

  1. Package imports

  2. MPAS preprocessing for visualization

    • Utility functions

    • Data loading

    • Triangular mesh generation using MPAS’s cell connectivity array from the primal mesh

  3. Interactive Holoviz Plots









Not necessary for plotting but useful for adding features





Not necessary for interactive plotting but useful for understanding the data used



  • Time to learn: 60 minutes


import math as math

import cartopy.crs as ccrs
import dask.dataframe as dd
import geocat.datafiles as gdf  # Only for reading-in datasets
import geoviews.feature as gf  # Only for displaying coastlines
import holoviews as hv
import numpy as np
import pandas as pd
from holoviews import opts
from holoviews.operation.datashader import rasterize as hds_rasterize
from numba import jit
from xarray import open_mfdataset

n_workers = 1

MPAS Preprocessing

The MPAS data requires some preprocessing to get it ready for visualization such as implementation of a few utility functions, loading the data, and creating triangular mesh out of the data to rasterize.

Utility functions

def unzipMesh(x, tris, t):
    """Splits a global mesh along longitude.

    Examine the X coordinates of each triangle in 'tris'. Return an array of 'tris' where
    only those triangles with legs whose length is less than 't' are returned.

    x: numpy.ndarray
        x-coordinates of each triangle in 'tris'
    tris: numpy.ndarray
        Triangle indices for each vertex in the MPAS file, in counter-clockwise order
    t: float
        Threshold value
    return tris[
        (np.abs((x[tris[:, 0]]) - (x[tris[:, 1]])) < t)
        & (np.abs((x[tris[:, 0]]) - (x[tris[:, 2]])) < t)
def triArea(x, y, tris):
    """Computes the signed area of a triangle.

    x: numpy.ndarray
        x-coordinates of each triangle in 'tris'
    y: numpy.ndarray
        y-coordinates of each triangle in 'tris'
    tris: numpy.ndarray
        Triangle indices for each vertex in the MPAS file
    return ((x[tris[:, 1]] - x[tris[:, 0]]) * (y[tris[:, 2]] - y[tris[:, 0]])) - (
        (x[tris[:, 2]] - x[tris[:, 0]]) * (y[tris[:, 1]] - y[tris[:, 0]])
def orderCCW(x, y, tris):
    """Reorder triangles as necessary so they all have counter clockwise winding order.
    CCW is what Datashader and MPL require.

    x: numpy.ndarray
        x-coordinates of each triangle in 'tris'
    y: numpy.ndarray
        y-coordinates of each triangle in 'tris'
    tris: numpy.ndarray
        Triangle indices for each vertex in the MPAS file
    tris[triArea(x, y, tris) < 0.0, :] = tris[triArea(x, y, tris) < 0.0, ::-1]
    return tris
def createHVTriMesh(x, y, triangle_indices, var, n_workers=1):
    """Create a Holoviews Triangle Mesh suitable for rendering with Datashader

    This function returns a Holoviews TriMesh that is created from a list of coordinates, 'x'
    and 'y', an array of triangle indices that addresses the coordinates in 'x' and 'y', and
    a data variable 'var'. The data variable's values will annotate the triangle vertices

    x: numpy.ndarray
        Projected x-coordinates of each triangle in 'tris'
    y: numpy.ndarray
        Projected y-coordinates of each triangle in 'tris'
    triangle_indices: numpy.ndarray
        Triangle indices for each vertex in the MPAS file, in counter-clockwise order
    var: numpy.ndarray
        Data variable from which the triangle vertex values are read.
    n_workers: int
        Number of workers, for Dask
    # Declare verts array
    verts = np.column_stack([x, y, var])

    # Convert to pandas
    verts_df = pd.DataFrame(verts, columns=["x", "y", "z"])
    tris_df = pd.DataFrame(triangle_indices, columns=["v0", "v1", "v2"])

    # Convert to dask
    verts_ddf = dd.from_pandas(verts_df, npartitions=n_workers)
    tris_ddf = dd.from_pandas(tris_df, npartitions=n_workers)

    # Declare HoloViews element
    tri_nodes = hv.Nodes(verts_ddf, ["x", "y", "index"], ["z"])
    trimesh = hv.TriMesh((tris_ddf, tri_nodes))
    return trimesh
def triangulatePoly(verticesOnCell, nEdgesOnCell):
    """Triangulate MPAS dual mesh:

    Triangulate each polygon in a heterogenous mesh of n-gons by connecting
    each internal polygon vertex to the first vertex. Uses the MPAS
    auxilliary variables verticesOnCell, and nEdgesOnCell.

    The function is decorated with Numba's just-in-time compiler so that it is translated into
    optimized machine code for better peformance

    verticesOnCell: numpy.ndarray
        Connectivity array that stores the vertex indices that surround a given cell
    nEdgesOnCell: numpy.ndarray
        Number of edges on a given cell.

    # Calculate the number of triangles. nEdgesOnCell gives the number of vertices for each cell (polygon)
    # The number of triangles per polygon is the number of vertices minus 2.
    nTriangles = np.sum(nEdgesOnCell - 2)

    triangles = np.ones((nTriangles, 3), dtype=np.int64)
    nCells = verticesOnCell.shape[0]
    triIndex = 0
    for j in range(nCells):
        for i in range(nEdgesOnCell[j] - 2):
            triangles[triIndex][0] = verticesOnCell[j][0]
            triangles[triIndex][1] = verticesOnCell[j][i + 1]
            triangles[triIndex][2] = verticesOnCell[j][i + 2]
            triIndex += 1

    return triangles

Load data and coordinates

Currently, the 30-km resolution dataset is used in this example and is available at geocat-datafiles. However, the other resolutions of these data are stored on NCAR’s Glade data storage because of their size. Due to their size, the higher resolution data sets are only distributed with two variables in them:

  • relhum_200hPa: Relative humidity vertically interpolated to 200 hPa

  • vorticity_200hPa: Relative vorticity vertically interpolated to 200 hPa

The “relhum_200hPa” variable is computed on the MPAS ‘primal’ mesh, while “vorticity_200hPa” is computed on the MPAS ‘dual’ mesh.

# Load data
datafiles = (

primalVarName = "relhum_200hPa"
dualVarName = "vorticity_200hPa"
central_longitude = 0.0

ds = open_mfdataset(datafiles, decode_times=False)
primalVar = ds[primalVarName].isel(Time=0).values
dualVar = ds[dualVarName].isel(Time=0).values

# Fetch lat and lon coordinates for the primal and dual mesh.
lonCell = ds["lonCell"].values * 180.0 / math.pi
latCell = ds["latCell"].values * 180.0 / math.pi
lonCell = ((lonCell - 180.0) % 360.0) - 180.0

lonVertex = ds["lonVertex"].values * 180.0 / math.pi
latVertex = ds["latVertex"].values * 180.0 / math.pi
lonVertex = ((lonVertex - 180.0) % 360.0) - 180.0
Downloading file 'netcdf_files/MPAS/FalkoJudt/dyamond_1/30km/diag.2016-08-20_00.00.00_subset.nc' from 'https://github.com/NCAR/GeoCAT-datafiles/raw/main/netcdf_files/MPAS/FalkoJudt/dyamond_1/30km/diag.2016-08-20_00.00.00_subset.nc' to '/home/runner/.cache/geocat'.
Downloading file 'netcdf_files/MPAS/FalkoJudt/dyamond_1/30km/x1.655362.grid_subset.nc' from 'https://github.com/NCAR/GeoCAT-datafiles/raw/main/netcdf_files/MPAS/FalkoJudt/dyamond_1/30km/x1.655362.grid_subset.nc' to '/home/runner/.cache/geocat'.

Generate triangular mesh using MPAS connectivity information

Primal mesh

In this example, we use the MPAS cellsOnVertex auxilliary variable, which defines mesh connectivity for the MPAS grid. Specifically, this variable tells us the cell indices contained by each cell.


The benefits of this are twofold:

  1. We’re using the actual mesh description from the MPAS output file

  2. For large grid this is much faster than synthesizing the connectivity information (e.g. by triangulating them with, for example, Delaunay triangulation).

So, first let’s:

  • Get the triangle indices (i.e. MPAS connectivity),

  • Make sure it is all in counter-clockwise order,

  • “Unzip” the mesh along the longitude (for now, assuming the central longitude from the map projection is 0.0, i.e. cutting the mesh where longitude wraps around from -180.0 to 180.0)

  • Project vertices from geographic to PCS coordinates

  • Create Holoviews TriMesh


Indexing in MPAS starts from 1, not zero :-(

tris = ds.cellsOnVertex.values - 1

tris = orderCCW(lonCell, latCell, tris)

tris = unzipMesh(lonCell, tris, 90.0)

projection = ccrs.Robinson(central_longitude=central_longitude)
xPCS, yPCS, _ = projection.transform_points(ccrs.PlateCarree(), lonCell, latCell).T

trimesh = createHVTriMesh(xPCS, yPCS, tris, primalVar, n_workers=n_workers)

Dual mesh

In this example though, we use the MPAS verticesOnCell and nEdgesOnCell auxilliary variables, which defines mesh connectivity for the MPAS dual grid. A lot of details in the following code is similarv to those in the primal mesh’s case except triangulatePoly() wheere we decompose each cell into triangles since for the dual mesh, the data are located on triangle centers, which correspond to cell (polygon) vertices.

verticesOnCell = ds.verticesOnCell.values - 1
nEdgesOnCell = ds.nEdgesOnCell.values

tris_dual = triangulatePoly(verticesOnCell, nEdgesOnCell)

tris_dual = unzipMesh(lonVertex, tris_dual, 90.0)

projection = ccrs.Robinson(central_longitude=central_longitude)
xPCS_dual, yPCS_dual, _ = projection.transform_points(
    ccrs.PlateCarree(), lonVertex, latVertex

trimesh_dual = createHVTriMesh(
    xPCS_dual, yPCS_dual, tris_dual, dualVar, n_workers=n_workers

Interactive HoloViz Plots


Since the emphasis of these plots is the interactivity, we will not provide much detail on the features/arguments other than interactivity-related ones, but such details to some extent can still be found in the code comments.

HoloViz tools provide essential interactivity features such as panning, zooming, hovering, clickable/selectable legends, etc. on a plot.


The first step to achieve interactivity with HoloViz tools is to choose bokeh as the backend:


Let’s define keyword arguments that will be commonly used for all of the plots and their opts throughout. For that, the plotting arguments are aggregator=mean to use the average of node values for shading in the rasterization and precompute=True to cache the data internally; the opts arguments are nothing more than opting in to showing the colorbar and using a colormap called “coolwarm”:

plot_kwargs = {
    "aggregator": "mean",
    "precompute": True,

opts_kwargs = {
    "colorbar": True,
    "cmap": "coolwarm",

Holoviews’ options system: opts

HoloViz packages provide high-level visualization functions that allow the customization of plot features through optional arguments. Furthermore, the HoloViews options system allows customizing a plot from title to size, legend, axes, and more. This system works by calling the .opts() method through a HoloViews plot object. We will set the opts defaults below and then customize plots throughout the notebook via .opts(). Keep an eye on them!

    opts.Image(frame_width=600, data_aspect=1),

Pan & zoom

Bokeh-rendered HoloViz plots come with default pan and zoom (box & wheel), tools as well as save and reset options in the very right. Just look at the following plot for those features, which uses Datashader’s rasterization method to visualize the data.

rasterized = hds_rasterize(trimesh, **plot_kwargs)
rasterized.opts(**opts_kwargs) * gf.coastline(projection=projection)