It is the purpose of this paper to document the NCAR global model topography generation software for unstructured grids (NCAR_Topo (v1.0)). Given a model grid, the software computes the fraction of the grid box covered by land, the grid-box mean elevation (deviation from a geoid that defines nominal sea level surface), and associated sub-grid-scale variances commonly used for gravity wave and turbulent mountain stress parameterizations. The software supports regular latitude–longitude grids as well as unstructured grids, e.g., icosahedral, Voronoi, cubed-sphere and variable-resolution grids.

Accurate representation of the impact of topography on atmospheric flow is
crucial for Earth system modeling. For example, the hydrological cycle is
closely linked to topography and, on the planetary scale, waves associated
with the mid-latitude jets are very susceptible to the effective drag caused
by mountains

Log–log plot of spectral energy versus wave number

When performing a spectral analysis of high-resolution elevation data (e.g.,
black line in Fig.

Surface elevation in kilometers for a cross section along latitude
30

The component of topography that can not be represented by

According to linear theory, gravity waves can propagate in the vertical only
when their intrinsic frequency is lower than the Brunt–Väisälä
frequency

It is the purpose of this paper to document a software package (NCAR_Topo (v1.0)) that, given a
“raw” high-resolution global elevation data set, maps elevation data to any
unstructured global grid and separates the scales needed for TMS
and GWD parameterizations. This separation of scales is done through an
intermediate mapping of the raw elevation data to a 3000 m cubed-sphere grid
(

A schematic showing the regridding procedure. Red fonts refer to the
naming conventions for the grids:

The separation of scales is, in continuous space, conveniently introduced
using spherical harmonics. Assume that elevation (above sea level) is a
smooth continuous function, in which case it can be represented by a
convergent expansion of spherical harmonic functions of the form

For the separation of scales the spherical harmonic expansion is truncated at
wave number

Let

For each target grid cell

The separation of scales is done through the use of a quasi-isotropic
gnonomic cubed-sphere grid in a two-step regridding procedure: binning from
source grid

Any quasi-uniform spherical grid could, in theory, be used for the separation
of scales or, given the discontinuous/fractal nature of topography, a more
rigorous scale separation method such as wavelets or other techniques could
have been used. It is noted that the separation of scales through an
intermediate grid does not correspond exactly to a spectral transform
truncation (used in the previous section). The intent is to approximately
eliminate scales below what can be resolved on the intermediate grid. For
reasons that will become clear, we have chosen to use a gnomonic cubed-sphere
grid (see Fig.

For notational simplicity the cubed-sphere cells are identified with one
index

The raw elevation data are provided on a geoid such as the World Geodetic
System 1984 (WGS84) ellipsoid, whose center is located at the Earth's center.
Latitude and longitude locations use the WGS84 geodetic datum. Similarly,
elevation above sea level is defined as the deviation from the WGS84 geoid or
WGM96 (Earth Geopotential Model 1996) geoid for newer data sets. Global
weather/climate models typically assume that Earth is a sphere, so the
elevations at a certain latitude–longitude pair on the geoid are taken to be
the same on the sphere. The consequences of this approximation in the context
of limited-area models are discussed in

The “raw” elevation data are usually from a digital elevation model (DEM)
such as the GTOPO30, a 30 arcsec global data set from the United States
Geological Survey

The centers of the regular latitude–longitude grid cells for the “raw”
topographic data are denoted

These data are binned to the cubed-sphere intermediate grid by identifying in
which gnomonic cubed-sphere grid cell

Transform

Locate which cubed-sphere panel

pm

pm

pm

pm

pm

pm

Given the panel number the associated central angles

The indices of the cubed-sphere cell in which the center of the latitude–longitude grid cell is located are given by

The set of indices for which center points of regular latitude–longitude
grid cells are located in gnomonic cubed-sphere cell

When

The land fraction is also binned to the intermediate cubed-sphere grid,

An example of a non-convex control volume in variable-resolution CAM-SE. Vertices are filled circles and they are connected with straight lines.

To remain consistent with previous GTOPO30-based topography generation
software for CAM, all land fractions south of 79

The binning process is straightforward since the cubed-sphere grid is
essentially an equidistant Cartesian grid on each panel in terms of the
central angle coordinates. This step could be replaced by rigorous remapping
in terms of overlap areas between the regular latitude–longitude grid and the
cubed-sphere grid using the geometrically exact algorithm of

Schematic of the notation used to define the overlap between target
grid cell

The cell-averaged values of elevation and sub-grid-scale variances
(Var

Let the target grid consist of

Surface geopotential

Note that the computation of overlap areas

The average elevation and variance used for TMS in target grid cell

The appended superscript “raw” in

After smoothing the target grid elevation, the sub-grid-scale
variance for GWD could be recomputed as the smoothing operation will add
energy to the smallest wavelengths:

See discussion on the difference between using

As discussed in the Introduction, mapping the elevation to the target grid without further filtering to
remove the highest wave numbers usually leads to excessive spurious noise in
the simulations when using terrain-following coordinates.
Non-terrain-following coordinates such as the

While it is necessary to smooth topography to remove spurious grid-scale
noise, it potentially introduces two problems. Filtering will typically raise
ocean points near step topography to non-zero elevation. Perhaps the most
striking example is the Andes mountain range, which extends one or two grid
cells into the Pacific after the filtering operation
(Fig.

Difference between

The difference between GMTED2010 and GTOPO30 (left) elevation (in m) and (right) SGH30 (in m), respectively, on the intermediate 3 km cubed-sphere grid.

The difference between GMTED2010 and GTOPO30 topographic variables
for CAM-FV at approximately 1

As there is no standard procedure for smoothing topography, we leave it up to
the user to smooth the raw topography

The naming conventions for the topographic variables in the software and
NetCDF files are as follows:

Below the topography software has been applied to different dynamical core
grids in CAM, for example CAM-SE, which uses the spectral element dynamical
core from HOMME

As mentioned in Sect.

The implications of topography smoothing on SGH are problematic, as illustrated
in Fig.

However, when additional smoothing is applied to the grid-box mean topography
(thick blue line, Fig.

Many global models use GTOPO30 as the raw topography data; however, more
accurate data sets are available, such as GMTED2010. NCAR_Topo (v1.0) is set up
to use both GTOPO30 and GMTED2010 (with MODIS for land fraction) source data.
The differences between the raw 1 km data sets are discussed in detail in

The NCAR global model topography generation software for unstructured grids (NCAR_Topo (v1.0)) has been documented and example applications to CAM have been presented. The topography software computes sub-grid-scale variances using a quasi-isotropic separation of scales through the intermediate mapping of high-resolution elevation data to an equiangular cubed-sphere grid. The software supports structured or unstructured (e.g., variable resolution) global grids.

The source codes for the NCAR Global Model Topography Generation Software for
Unstructured Grids are available through GitHub. The repository URL is

NCAR is sponsored by the National Science Foundation (NSF). M. Taylor was supported by the Department of Energy Office of Biological and Environmental Research, work package 12-015334 “Multiscale Methods for Accurate, Efficient, and Scale-Aware Models of the Earth System”. Thanks to Sang-hun Park (NCAR) for providing data for the GTOPO30 power spectrum. Thanks to Max Suarez (NASA) for encouraging upgrading to the GMTED2010 data. We thank the two reviewers for their useful comments. Partial support for this work was provided through the Scientific Discovery through Advanced Computing (SciDAC) program funded by U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research.Edited by: S. Valcke