Manuscript prepared for Geosci. Model Dev.with version 2014/07/29 7.12 Copernicus papers of the LATEX class coperni-cus.cls.Date: 12 May 2015

NCAR Global Model Topography Generation Software forUnstructured GridsPeter H. Lauritzen1, Julio T. Bacmeister1, Patrick F. Callaghan1, and Mark A. Taylor21National Center for Atmospheric Research, 1850 Table Mesa Drive, Boulder, Colorado, USA2Sandia National Laboratories, Albuquerque, New Mexico, USA

Correspondence to: Peter Hjort Lauritzen(pel@ucar.edu)

Abstract. It is the purpose of this paper to document theNCAR global model topography generation software for un-structured grids. Given a model grid, the software computesthe fraction of the grid box covered by land, the gridboxmean elevation, and associated sub-grid scale variances com-5monly used for gravity wave and turbulent mountain stressparameterizations. The software supports regular latitude-longitude grids as well as unstructured grids; e.g. icosahe-dral, Voronoi, cubed-sphere and variable resolution grids.

As an example application and in the spirit of document-10ing model development, exploratory simulations illustrat-ing the impacts of topographic smoothing with the NCAR-DOE CESM (Community Earth System Model) CAM5.2-SE(Community Atmosphere Model version 5.2 - Spectral Ele-ments dynamical core) are shown.15

1 Introduction

Accurate representation of the impact of topography on at-mospheric flow is crucial for Earth system modeling. For ex-ample, the hydrological cycle is closely linked to topographyand, on the planetary scale, waves associated with the mid-20latitude jets are very susceptible to the effective drag causedby mountains (e.g., Lott and Miller, 1997). Despite the factthat surface elevation is known globally with a high levelof precision, the representation of its impact on atmosphericflow in numerical models remains a challenge.25

When performing a spectral analysis of high resolutionelevation data (e.g., black line in Figure 1), it is clearthat Earth’s topography decreases quite slowly with increas-ing wave number (see also Balmino, 1993; Uhrner, 2001;Gagnon et al., 2006). Consequently, at any practical model30resolution there will always be a non-negligible spectral

component of topography present near the grid scale andthere will always be a non-negligible spectral component oftopography below the grid-scale (sub-grid-scale component).The resolved scale component is the mean elevation in each35grid box h, or, equivalently1, the surface geopotential Φs. Itis common practice not to force the highest wave numbersdirectly in the model to alleviate obvious spurious noise (e.g.Navarra et al., 1994; Lander and Hoskins, 1997). Hence Φsis usually smoothed. Figure 1 shows the power spectrum for40surface elevation for different levels of smoothing of topog-raphy in the NCAR-DOE CESM (Community Earth SystemModel) CAM (Community Atmosphere Model; Neale et al.,2010) SE (Spectral Element; Thomas and Loft, 2005; Den-nis et al., 2005) and CAM-FV (Finite-Volume; Lin, 2004).45Figure 2 shows the associated elevations for a cross sectionthrough the Andes mountains. The amount of smoothing nec-essary is intrinsically linked to the numerical methods anddiscretization choices in the dynamical core. Further discus-sion on Φs smoothing is given in Section 3.2.50

The component of topography that can not be representedby Φs is referred to as sub-grid-scale topography. Sub-grid-scale processes may be sub-grid flow blocking, flow splitting,sheltering effects, generation of turbulence by roughness andgravity wave breaking (e.g., Bougeault et al., 1990). These55processes can have an important impact on the resolvedscale flow. Global models usually have a parameterization forgravity wave drag (GWD) (e.g., Eckermann and Chun, 2003)and turbulent effects referred to as turbulent mountain stress(TMS). An increasing number of models also have a low-60level blocking parameterization (e.g., Lott and Miller, 1997;Webster et al., 2003; Zadra et al., 2003; Kim and Doyle,2005; Scinocca and McFarlane, 2000) and incorporate the ef-fects of sub-grid-scale topographic anisotropy (i.e. the exis-

1if gravity is assumed constant

2 Lauritzen et al.: NCAR topography software

Figure 1. Log/log plot of spectral energy versus wave number Kfor the ‘raw’ 1km USGS data (GTOPO30), different levels ofsmoothing for 100km CAM-SE topography, and CAM-FV. Labels‘04x’, ‘08x’, ’16x’ and ‘32x’ CAM-SE, refer to different levels ofsmoothing, more precisely, four, eight, sixteen and thirty two ap-plications of a ‘Laplacian’ smoothing operator in CAM-SE, respec-tively. Label ‘CAM-FV’ refers to the topography used in CAM-FVat 0.9◦×1.25◦ resolution. ‘0x’ CAM-SE is the unsmoothed topog-raphy on an approximately 1◦ grid CAM-SE grid. Note that the blue(4x, CAM-SE) and brown (CAM-FV) lines are overlaying. Solidstraight line shows the K−2 slope. The associated surface eleva-tions are shown on Figure 2.

tence of ridges with dominant orientations used to determine65the direction and magnitude of the drag exerted by sub-gridtopography). The importance of anisotropy in quantifying to-pographic effects has been recognized for some time (e.g.,Baines and Palmer, 1990; Bacmeister, 1993).

According to linear theory gravity waves can propagate in70the vertical only when their intrinsic frequency is lower thanthe the Brunt-Väisälä frequency N (e.g., Durran, 2003). Fororographically-forced gravity waves the intrinsic frequencyis set by the obstacle horizontal scale and the wind speed.When obstacle scales are too small to generate propagat-75ing waves we expect drag to produced by unstratified turbu-lent flow, a process which is typically parameterized in mod-els’ TMS schemes. For larger obstacles we expect both dragand vertically-propagating waves to result, processes which

Figure 2. Surface elevation in kilometers for a cross section alonglatitude 30◦S (through Andes mountain range) for different repre-sentations of surface elevation. The labeling is the same as in Figure1.

are dealt by GWD schemes. Unfortunately the scale separat-80ing TMS and GWD processes is flow dependent. For typi-cal midlatitude values of low-level wind (10 ms−1) and N(10−2s−1) waves with wavelengths less than around 6000mwill not propagate in the vertical. A separation scale of 5000m has been used by ECMWF (1997); Beljaars et al. (2004).85Here we will generate two sub-grid-scale variables derivedfrom the topography data: The variance of topography belowthe 6000m scale (referred to as V ar(TMS)) and the varianceof topography with a scale longer than 6000m and less thanthe grid scale (referred to as V ar(GWD)).90

It is the purpose of this paper to document a softwarepackage that, given a ‘raw’ high resolution global elevationdataset, maps elevations data to any unstructured global gridand consistently separates the scales needed for TMS andGWD parameterizations. This separation of scales is done95through an intermediate mapping of the raw elevation data toa 3000 m cubed-sphere grid (Λ→A) before mapping fieldsto the target model grid (A→ Ω) as schematically shown onFigure 3. This two-step process is described in section 2.2 af-ter a mathematical definition of the scale-separation (section1002.1). In section 2.2.3 we briefly discuss Φs smoothing. In thespirit of model development some exploratory experimentsillustrating the impacts of topographic smoothing with theNCAR-DOE CAM-SE and, for comparison CAM-FV, arepresented in section 3.2. Results from these experiments are105shown to emphasize the importance of topographic smooth-

Lauritzen et al.: NCAR topography software 3

ing rather than detailed investigation of the accuracy and pro-cess level analysis of how to most accurately model flow overtopography.

2 Method110

2.1 Continuous: separation of scales

The separation of scales is, in continuous space, convenientlyintroduced using spherical harmonics. Assume that eleva-tion (above sea level) is a smooth continuous function inwhich case it can be represented by a convergent expansion115of spherical harmonic functions of the form

h(λ,θ) =

∞∑m=−∞

∞∑n=|m|

ψm,nYm,n(λ,θ), (1)

(e.g., Durran, 2010) where λ and θ are longitude and latitude,respectively, ψm,n are the spherical harmonic coefficients.Each spherical harmonic function is given in terms of the120associated Legendre polynomial Pm,n(θ):

Ym,n = Pm,n(θ)eimλ (2)

wherem is the zonal wave number andm−|n| is the numberof zeros between the poles and can therefore be interpretedas meridional wave number.125

For the separation of scales the spherical harmonic expan-sion is truncated at wave number M

h(M)(λ,θ) =

∞∑m=−M

M∑n=|m|

ψ(M)m,nYm,n(λ,θ), (3)

where a triangular truncation, which provides a uniform spa-tial resolution over the entire sphere, is used.130

Let h(tgt)(λ,θ) be a continuous representation of the ele-vation containing the spatial scales of the target grid. We donot write h(tgt)(λ,θ) explicitly in terms of spherical harmon-ics as the target grid may be variable resolution and thereforecontains different spatial scales in different parts of the do-135main.

For each target grid cell Ωk, k = 1, ..,Nt, where Nt is thenumber of target grid cells, define the variances

Var(tms)Ωk =∫∫Ωk

[h(M)(λ,θ)−h(λ,θ)

]2cos(θ)dλdθ, (4)

Var(gwd)Ωk =∫∫Ωk

[h(tgt)(λ,θ)−h(M)(λ,θ)

]2cos(θ)dλdθ.(5)140

So Var(tms)Ωk is the variance of elevation on scales below wave

numberM and Var(gwd)Ωk is the variance of elevation on scaleslarger than wave number M and below the target grid scale.

2.2 Discrete: separation of scales

The separation of scales is done through the use of a quasi-145isotropic gnonomic cubed-sphere grid in a two-step regrid-ding procedure : binning from source grid Λ to intermediategrid A (separation of scales) and then rigorously remap vari-ables to the target grid Ω.

Any quasi-uniform spherical grid could, in theory, be used150for the separation of scales. For reasons that will becomeclear we have chosen to use a gnomonic cubed-sphere grid(see Figure 3) resulting from an equi-angular gnomonic (cen-tral) projection

x= r tanα and y = r tanβ; α,β ∈[−π

4,π

4

], (6)155

(Ronchi et al., 1996) where α and β are central anglesin each coordinate direction, r =R/

√3 and R is the ra-

dius of the Earth. A point on the sphere is identified withthe three-element vector (x,y,ν), where ν is the panelindex. Hence the physical domain S (sphere) is repre-160sented by the gnomonic (central) projection of the cubed-sphere faces, Ω(ν) = [−1,1]2, ν = 1,2, . . . ,6, and the non-overlapping panel domains Ω(ν) span the entire sphere:S =

⋃6ν=1 Ω

(ν). The cube edges, however, are discontinu-ous. Note that any straight line on the gnomonic projection165(x,y,ν) corresponds to a great-circle arc on the sphere. Inthe discretized scheme we let the number of cells along a co-ordinate axis be Nc so that the total number of cells in theglobal domain is 6×N2c . The grid lines are separated by thesame angle ∆α= ∆β = π2Nc in each coordinate direction.170

For notational simplicity the cubed-sphere cells are iden-tified with one index i and the relationship between i and(icube,jcube,ν) is given by

i= icube+ (jcube− 1)Nc + (ν− 1)N2c , (7)

where (icube,jcube) ∈ [1, ..,Nc]2 and ν ∈ [1,2, ..,6]. In175terms of central angles (α,β) the cubed-sphere grid cell iis defined as

Ai = [(icube− 1)∆α−π/4, icube∆α−π/4]×[(jcube− 1)∆β−π/4, jcube∆β−π/4], (8)180

and ∆Ai denotes the associated spherical area. A formulafor the spherical area ∆Ai of a grid cell on the gnomoniccubed-sphere grid can be found in Appendix C of Lauritzenand Nair (2008) (note that equation C3 is missing arccos on185the right-hand side). A quasi-uniform approximately 3000 mresolution is obtained by using Nc = 3000 which results in ascale separation of roughly 6000 m. For more details on theconstruction of the gnomonic grid see, e.g., Lauritzen et al.(2010).190

2.2.1 Step 1: raw elevation data to intermediate cubed-sphere grid (Λ → A)

The ‘raw’ elevation data is usually from a digital elevationmodel (DEM) such as the GTOPO30; a 30 arc second global

4 Lauritzen et al.: NCAR topography software

(lat−lon grid)

of 30sec h)

Ω

Target grid

Raw data

Binning

Any

unstructured

Remapping

structured or

grid

USGS 30sec (~1km) resolution n=3000 (~3km)

PHIS

variables:

LANDFRACSGH30SGH(standard deviation of ~3km cubed−sphere h)

(land fraction [0,1])LANDFRAC

h(height in m)

variables:

PHIS(surface geopotential)LANDFRACSGH30

variables:

(standard deviation

MPAS

CAM−SE

ΑΛ

cubed−sphere gridIntermediate

Figure 3. A schematic showing the regridding procedure. Red fonts refer to the naming conventions for the grids: Λ is the ‘raw’ data grid( 1km regular lat-lon grid), A is the intermediate cubed-sphere grid and Ω is the target grid which may be any unstructured or structuredgrid. The variable naming convections in the boxes are explained in section 2.3. Data for the variable resolution MPAS (Model for PredictionAcross Scales; Skamarock et al., 2012) grid plot is courtesy of W. C. Skamarock (NCAR).

dataset from the United States Geological Survey (USGS;195Gesch and Larson, 1998) defined on an approximately 1kmregular latitude-longitude grid. Several newer, more accurate,and locally higher resolution elevation datasets are avail-able such as GLOBE (GLOBE Task Team and others, 1999)and the NASA Shuttle Radar Topographic Mission (SRTM)200DEM data (Farr et al., 2007). The SRTM data, however, isonly near-global (up to 60◦ North and South). Here we useGTOPO30. The data comes in 33 tiles (separate files) in 16-bit binary format. Fortran code is provided to convert the datainto one NetCDF file. Even though the elevation is stored as205integers the size of the NetCDF file is 7GB. The GTOPOfile contains height h and landfraction LANDFRAC (forthe mathematical operations below we use f to refer to landfraction).

The center of the regular latitude-longitude grid cells for210the ‘raw’ topographic data are denoted (λilon,θjlat), ilon=1, ...,nlon, jlat= 1, ...,nlat. For the USGS dataset usedhere nlon= 43200 and nlat= 21600. As for the cubed-sphere we use one index j to reference the grid cells

j = ilon+ (jlat− 1)×nlon, j ∈ [1, ...,Nr], (9)215

where Nr = nlon×nlat. The spherical area of grid cell Λjis denoted ∆Λj and the average elevation in cell j is givenby h(raw)Λj .

This data is binned to the cubed-sphere intermediate gridby identifying in which gnomonic cubed-sphere grid cell220(λilon,θjlat) is located. Due to the ‘Cartesian’-like structureof the cubed-sphere grid the search algorithm is straight for-ward (following Nair et al., 2005):

– transform (λilon,θilat) coordinate to Cartesian coordi-nates (x,y,z):225

x = cos(λilon) cos(θjlat),

y = sin(λilon) cos(θjlat),

z = sin(θilat).

– locate which cubed-sphere panel (λilon,θilat) is locatedon through a ‘coordinate maximality’ algorithm, i.e. let230

pm= max(|x|, |y|, |z|) ,

then if

Lauritzen et al.: NCAR topography software 5

– pm= |x| and x > 0 then (λilon,θilat) is on ν = 1.– pm= |y| and y > 0 then (λilon,θilat) is on ν = 2.– pm= |x| and x < 0 then (λilon,θilat) is on ν = 3.235– pm= |y| and y < 0 then (λilon,θilat) is on ν = 4.– pm= |z| and z ≤ 0 then (λilon,θilat) is located on

the bottom panel, ν = 5.

– pm= |z| and z > 0 then (λilon,θilat) is located onthe top panel, ν = 6.240

– Given the panel number the associated central angles(α,β) are given by:

– ν = 1: (α,β) =[arctan

(xz

),arctan

(yz

)].

– ν = 2: (α,β) =[arctan

(−xy

),arctan

(zy

)].

– ν = 3: (α,β) =[arctan

(−y−x

),arctan

(y−x

)].245

– ν = 4: (α,β) =[arctan

(x−y

),arctan

(z−y

)].

– ν = 5: (α,β) =[arctan

(y−z

),arctan

(x−z

)].

– ν = 6: (α,β) =[arctan

(yz

),arctan

(−xz

)].

– the indices of the cubed-sphere cell in which the centerof the latitude-longitude grid cell is located is given by250

icube = CEILING

(α+ π4∆α

),

jcube = CEILING

(β+ π4∆β

),

where the CEILING(·) function returns the smallest in-teger not less than the argument.

The set of indices for which center points of regular latitude-255longitude grid cells are located in gnomonic cubed-spherecell Ai is denoted Si. Note that since the USGS dataset ishigher resolution that the cubed-sphere Si is guaranteed tobe non-empty. Through this binning process the approximateaverage elevation in cubed-sphere cell i becomes260

h(cube)

Ai =1

∆Ai

∑j∈Si

h(raw)Γj

∆Λj . (10)

When h(cube)

Ai is known we can compute the sub-grid vari-ance on the intermediate cubed-sphere grid A:

V ar(tms)Ai

=1

∆Ai

∑j∈Si

(h

(cube)

Ai −h(raw)Γj

)2∆Λj . (11)

The land fraction is also binned to the intermediate cubed-265sphere grid

f(cube)

Ai =1

∆Ai

∑j∈Si

f(raw)Γj

∆Λj . (12)

To remain consistent with previous topography generationsoftware for CAM all landfractions South of 79◦S are set toone which effectively extends the land for the Ross Ice shelf.270

The binning process is straight forward since the cubed-sphere grid is essentially an equidistant Cartesian grid oneach panel in terms of the central angle coordinates. This stepcould be replaced by rigorous remapping in terms of over-lap areas between the regular latitude-longitude grid and the275cubed-sphere grid using the geometrically exact algorithmof (Ullrich et al., 2009) optimized for the regular latitude-longitude and gnomonic cubed-sphere grid pair or the moregeneral remapping algorithm called SCRIP (Jones, 1999).

2.2.2 Step 2: cubed-sphere grid to target grid (A → Ω)280

The cell averaged values of elevation and sub-grid-scale vari-ances (V ar(tms)Ω and V ar

(gwd)Ω ) on the target grid are com-

puted by rigorously remapping the variables from the cubed-sphere grid to the target grid. The remapping is performedusing CSLAM (Conservative Semi-LAgrangian Multi-tracer285transport scheme) technology (Lauritzen et al., 2010) that hasthe option for performing higher-order remapping. It is pos-sible to use large parts of the CSLAM technology since thesource grid is a gnomonic cubed-sphere grid hence insteadof remapping between the gnomonic cubed-sphere grid and290a deformed Lagrangian grid, as done in CSLAM transport,the remapping is from the gnomonic cubed-sphere grid toany target grid constructed from great-circle arcs (the targetgrid ‘plays the role’ of the Lagrangian grid). However, a cou-ple of modifications where made to the CSLAM search algo-295rithm. First of all, the target grid cells can have an arbitrarynumber of vertices whereas the CSLAM transport search al-gorithm assumes that the target grid consists of quadrilater-als and the number of overlap areas are determined by thedeformation of the transporting velocity field. In the case300of the remapping needed in this application the target gridconsists of polygons with any number of vertices and thesearch is not constrained by the physical relation betweenregular and deformed upstream quadrilaterals. Secondly, theCSLAM search algorithm for transport assumes that the tar-305get grid cells are convex which is not necessarily the case fortarget grids. The CSLAM search algorithm has been mod-ified to support non-convex cells that are, for example, en-countered in variables resolution CAM-SE (see Figure 4);essentially that means that any target grid cell may cross a310gnonomic isoline (source grid line) more than twice.

Let the target grid consist ofNt grid cells Ωk, k = 1, ...,Ntwith associated spherical area ∆Ωk. The search algorithm forCSLAM is used to identify overlap areas between the targetgrid cell Ωk and the cubed-sphere grid cells A`, `= 1, ..,Nc.315Denote the overlap area between Ωk and A`

Ωk` = Ωk ∩A`, (13)

(see Figure 5) and let Lk denote the set of indices for whichΩk ∩A`, `= 1, ..,Nc, is non-empty. Then the average eleva-

6 Lauritzen et al.: NCAR topography software

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������ ������ ������ ����� ������ ������ ������ ������

����������������

��

�������������������

Figure 4. An example of a non-convex control volume in variableresolution CAM-SE. Vertices are filled circles and they are con-nected with straight lines.

k

Al

Ω

Ω

kl

Figure 5. Schematic of the notation used to define the overlap be-tween target grid cell Ωk (red polygon) and high resolution cubed-sphere grid cell A` (Cartesian-like grid on Figure). The overlaparea, Ωk` = Ωk ∩A`, is shaded with cross-hatch pattern on Figure.

tion and variance used for TMS in target grid cell k are given320by

h(tgt,raw)

Ωk=

1

∆Ωk

∑`∈Lk

h(cube)

A`∆Ωk`, (14)

V ar(tms)

Ωk=

1

∆Ωk

∑`∈Lk

V ar(tms)

Ω`∆Ωk`, (15)

respectively. The variance of the cubed-sphere data h(cube)

with respect to the target grid cell average values h(tgt,raw)

325

is given by

V ar(gwd,raw)

Ωk=

1

∆Ωk

∑`∈Lk

(h

(tgt,raw)

Ωk−h(cube)A`

)2∆Ωk`,

(16)

The appended superscript raw in h(tgt,raw)

andV ar

(gwd,raw)refers to the fact that the elevation and

GWD variance is based on unsmoothed elevation. As men-330tioned in the introduction the elevation is usually smoothedi.e. the highest wave number are removed. This smoothedelevation is denoted

h(tgt,smooth)

. (17)

Note that after smoothing the target grid elevation the sub-335grid scale variance for GWD should be recomputed as thesmoothing operation will add energy to the smallest wavelenghts:

V ar(gwd,smooth)

Ωk=

1

∆Ωk

∑`∈Lk

(h

(tgt,smooth)

Ωk−h(cube)A`

)2∆Ωk`.

(18)

The smoothing of elevation is discussed in some detail in the340next section.

2.2.3 Smoothing of elevation h(tgt)Ω

As discussed in the introduction the raw topographic datamapped to the target grid without further filtering to removethe highest wave numbers usually leads to excessive spurious345noise in the simulations. There seem to be no standardizedprocedure, for example a test case suite, to objectively selectthe level of smoothing and filtering method. The amount ofsmoothing necessary to remove spurious noise in, e.g. ver-tical velocity, depends on the amount of inherent or explicit350numerical diffusion in the dynamical core (e.g., Lauritzenet al., 2011). It may be considered important that the topo-graphic smoothing is done with discrete operators consistentwith the dynamical core.

While it is necessary to smooth topography to remove355spurious grid-scale noise, it potentially introduces two prob-lems. Filtering will typically raise ocean points near step to-pography to non-zero elevation. Perhaps the most strikingexample is the Andes mountain range that extends one ortwo grid cells into the Pacific after the filtering operation360(Figure 2). Ocean and land points are treated separately inweather/climate models so raised sea-points may potentiallybe problematic. Secondly, the filtering will generally reducethe height of local topographic maxima and given the impor-tance of barrier heights in atmospheric dynamics, this could365be a problem for the global angular momentum budget andcould fundamentally change the flow (unless a parameteri-zation for blocking is used). To capture more of the barriereffect (blocking) , two approaches have been put forwardin the literature to deepen valleys and increase peak heights370while filtering out small scales: envelope topography adjuststhe surface height with sub-grid scale topographic variance(Wallace et al., 1983; Mesinger and Strickler, 1982). Looselyspeaking, the otherwise smoothed peak heights are raised.

Lauritzen et al.: NCAR topography software 7

This process may perturb the average surface height. Alter-375natively, one may use Silhouette averaging that adds mass... (Smart et al., 2005; Walko and Tremback, 2004; Bossert,1990). A similar approach, but implemented as variationalfiltering, is taken in Rutt et al. (2006); this method also im-poses additional constraints such as enforcing zero elevation380over ocean masks.

As there is no standard procedure for smoothing topog-raphy, we leave it up to the user to smooth the raw topog-raphy h

(tgt,raw). The smoothed topography is referred to as

h(tgt,smooth)

. As mentioned before V ar(gwd,smooth)

Ωkmust be385

recomputed after smoothing h as the filtering operation willtransfer energy to the sub-grid-scale.

2.3 Naming conventions

The naming conventions for the topographic variables in thesoftware and NetCDF files is:390

PHIS = gh(tgt)

Ω , (19)

SGH =

√V ar

(gwd)Ω , (20)

SGH30 =

√V ar

(tms)Ω , (21)

LANDFRAC = f(tgt)

Ω , (22)

where g is the gravitational constant.395

3 Results

Exploratory simulations illustrating the effects of topo-graphic smoothing on some climate diagnostics in CAM areshown.

3.1 Smoothing methods used in CAM-FV and CAM-SE400

In the CAM-FV the highest wave-numbers are removedby mapping Φs (surface geopotential) to a regular latitude-longitude grid that is half the resolution of the desired modelresolution, and then map back to the model grid by one-dimensional remaps along latitudes and longitudes, respec-405tively, using the PPM (Piecewise Parabolic Method) withmonotone filtering. In CAM-SE the surface geopotential issmoothed by multiple applications of the CAM-SE Laplaceoperator combined with a bounds preserving limiter. Figure2 shows different levels of smoothing of surface height for410CAM-SE and for comparison CAM-FV. It can clearly beseen that there are large differences between the height of themountains with different smoothing operators and smoothingstrength.

3.2 Example topography smoothing experiments with415CAM-SE

CAM-SE uses the spectral element dynamical core fromHOMME (High-Order Method Modeling Environment;

Thomas and Loft, 2005; Dennis et al., 2005). CESM tagcesm1_1_0_rel06 with the FAMIPC5 compset is used4202. The model is run at approximately 1◦ resolution whichis the NE30NP4 configuration with 30×30 elements oneach cubed-sphere panel and 4×4 Gauss-Lobatto-Legendre(GLL) quadrature points in each element. The default hyper-viscosity coefficient is ν = 1× 1015m4/s.425

Results are shown for 30 year AMIP-style runs (CESMFAMIPC5 compset). Simulation were performed with differ-ent levels of smoothing of topography and changes to thedivergence damping parameter. The level of smoothing fol-lows the naming convention defined in the caption of Figure4301. The 1 x div refers to the same level of damping of vor-tical and divergent modes (fourth-order hyperviscosity withdamping coefficient ν = 1×1015m4/s). Experiments are runfor which the divergent modes are damped with a coefficientthat is 2.52 and 52 times larger than the damping coefficient435for the vortical modes.

Figure 7 shows results from AMIP simulations with CAM-SE using different levels of Φs smoothing and numerical dif-fusion of divergent modes. Spurious noise near steep topog-raphy is apparent in vertical velocity ω (top panels) for model440configurations with weak smoothing and divergence damp-ing. Effects on important hydrological fields such as precipi-tation are also evident although they are somewhat less pro-nounced. As already noted, there are not commonly acceptedmeasures of what constitutes a reasonable level of apparently445spurious small-scale variability in climate simulation vari-ables. Smoothing of topography can itself have negative ef-fects. We note for example in the precipitation plots shown inFigure 7 that smoothing Φs does nothing to remove the largemoist bias present over the Himalayan front, in fact smooth-450ing is arguably increasing the extent of the bias. The detaileddynamics behind these improvements is not yet understood,but there connection to rougher topography is clear.

Figure 8 shows the total kinetic energy spectra (TKE) forthe different model configurations. The energy associated455with vortical modes is not significantly by the roughness ofthe topography or the strength of the divergence damping.Obviously the energy associated with divergent modes is di-rectly related to the divergence damping coefficient but theroughness of the topography does not appear to have any sig-460nificant effect on the tail of the TKE energy spectrum for di-vergence (these results, however, may change at higher hori-zontal resolutions).

4 Conclusions

The NCAR global model topography generation software for465unstructured grids has been documented and example appli-cations to CAM have been presented. The topography soft-ware consistently computes sub-grid scale variances using aquasi-isotropic separation of scales through the intermediate

2CAM version 5.2 in which SE uses Eulerian vertical advection

8 Lauritzen et al.: NCAR topography software

Figure 6. Surface geopotential Φs (upper left), SGH (upper right), SGH30 (lower left) and LANDFRAC (lower right) for CAM-SENE30NP4 resolution. The data is plotted on the native grid. NCL scripts to create this Figure are released with the software source code.

mapping of high resolution elevation data to an equi-angular470cubed-sphere grid. The software supports structured or un-structured (e.g., variable resolution) global grid.

Code availability

The source codes for the NCAR Global Model TopographyGeneration Software for Unstructured Grid are available at475through Github. The repository URL is https://github.com/UCAR/Topo/tags/. The repository also contains NCL scriptsto plot the topography variables (Figure 6) that the softwaregenerates.

Acknowledgements. NCAR is sponsored by the National Science480Foundation (NSF). Mark Taylor was supported by the Departmentof Energy Office of Biological and Environmental Research, workpackage 12-015334 ‘Multiscale Methods for Accurate, Efficient,and Scale-Aware Models of the Earth System’. Thanks to Sang-hunPark (NCAR) for providing data for the GTOPO30 power spectrum.485

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