Abstract

The authors evaluate the climate produced by the Community Climate System Model, version 4, running with the new spectral element atmospheric dynamical core option. The spectral element method is configured to use a cubed-sphere grid, providing quasi-uniform resolution over the sphere and increased parallel scalability and removing the need for polar filters. It uses a fourth-order accurate spatial discretization that locally conserves mass and total energy. Using the Atmosphere Model Intercomparison Project protocol, the results from the spectral element dynamical core are compared with those produced by the default finite-volume dynamical core and with observations. Even though the two dynamical cores are quite different, their simulated climates are remarkably similar. When compared with observations, both models have strengths and weaknesses but have nearly identical root-mean-square errors and the largest biases show little sensitivity to the dynamical core. The spectral element core does an excellent job reproducing the atmospheric kinetic energy spectra, including fully capturing the observed Nastrom–Gage transition when running at 0.125° resolution.

1. Introduction

Here we report on the climate produced by a spectral element atmospheric dynamical core option within the Community Climate System Model (CCSM), version 4. The CCSM is a state-of-the-art climate model with atmosphere, ocean, land, and ice component models that exchange information through a flux coupler (Gent et al. 2011). The spectral element dynamical core comes from the High-Order Method Modeling Environment (HOMME; Dennis et al. 2005, 2012), which has been integrated into the CCSM Community Atmosphere Model (CAM). The standalone HOMME model is also used for research into other numerical methods, such as discontinuous-Galerkin (Nair 2009), adaptive mesh refinement (St-Cyr et al. 2008), and implicit time integration (Evans et al. 2010). We refer to CAM with the spectral element dynamical core as CAM-SE, CAM with the default finite volume dynamical core (Neale et al. 2011, manuscript submitted to J. Climate) as CAM-FV, and CAM with the Eulerian global spectral method (Collins et al. 2006) option as CAM-EUL.

CAM-SE is capable of using fully unstructured grids. Support for unstructured grids and the integration of the spectral element method in CAM was made possible by the decoupling of dynamics and physics used in CAM’s process split approach (Williamson 2002), the extensive infrastructure work to support unstructured grids (Worley and Drake 2005), and the CCSM tri-grid capability (Craig et al. 2012), which allows different grids for the atmosphere, land, and ice/ocean components. The spectral element method was chosen for integration into CAM based on its demonstrated scalability when run as a standalone dynamical core. The high-order finite element structure of the method also makes it well suited to upcoming heterogeneous computer architectures (Carpenter et al. 2012). In addition to scalability, the spectral element method is known to produce accurate solutions for atmospheric problems, as demonstrated first with shallow-water test cases (Taylor et al. 1997; Thomas and Loft 2002), three-dimensional dry dynamical test cases (Taylor et al. 1998; Thomas and Loft 2005; Dennis et al. 2005; Taylor et al. 2007; Lauritzen et al. 2010), multicloud simulations (Khouider et al. 2011), aquaplanet experiments that include full physics (Taylor et al. 2008; Mishra et al. 2011a,b), and realistic simulations with CAM2 physics (Wang et al. 2007). The SE method has also been pursued for global forecast modeling, as in Giraldo and Rosmond (2004), Giraldo (2005), and Kim et al. (2008).

The goal of this work is to build confidence in CAM-SE to justify devoting future model development and computational resources targeting high-resolution simulations that are made possible by the parallel scalability of CAM-SE. We first give an overview of the spectral element dynamical core used in CAM-SE (section 2), and then compare CAM4 simulations produced by CAM-SE, CAM-FV, and observations. We compare the kinetic energy spectra (section 5) and mean climate (section 6) and discuss some transient features (section 7) and regional climate details (section 8), using 1° or equivalent resolutions. For the spectra, we also include results from aquaplanet and the CAM-EUL simulations with up to 0.125° resolutions.

2. The CAM spectral element dynamical core

CAM-SE uses a continuous Galerkin spectral finite-element method (Taylor et al. 1997; Fournier et al. 2004; Thomas and Loft 2005; Wang et al. 2007; Taylor and Fournier 2010), commonly referred to as the spectral element method. These classes of methods were designed from inception for fully unstructured grids. For the simulations presented here, the goal is global uniform resolution so we use the cubed-sphere grid (Fig. 1) first used in Sadourny (1972), with the equal-angle projection (Rančić et al. 1996). This represents a large change in the horizontal grid as compared to CAM’s other dynamical core options, but most other aspects of CAM-SE are based on a combination of well-tested approaches from CAM-EUL and CAM-FV. CAM-SE tracer transport is modeled closely on CAM-FV; it uses the same conservation form of the transport equation and the same vertically Lagrangian discretization (Lin 2004). CAM-SE dynamics (momentum, temperature, and surface pressure) are modeled closely on CAM-EUL; they share the same vertical coordinate, vertical discretization, hyperviscosity-based horizontal diffusion, and top-of-model dissipation and solve the same moist hydrostatic equations. CAM-SE (like FV) uses the vector-invariant form of the momentum equation instead of the vorticity-divergence formulation. The CAM-SE discretization provides several benefits compared to CAM-FV and CAM-EUL. As with all methods on quasi-uniform grids, avoiding the inherently load-imbalanced polar filter allows for efficient, fixed two-dimensional domain decomposition, resulting in significantly improved scaling on parallel computers. Such improved scaling was one of the motivations for migration to the cubed-sphere grid in Donner et al. (2011), and improved scaling in CAM is also expected from FV methods designed for unstructured grids (Putman and Lin 2007, 2009; Ringler et al. 2011). CAM-SE also improves CAM’s numerical conservation: it locally conserves (at the element level) mass, tracer mass, and moist total energy without the use of ad hoc fixers, and the horizontal momentum advection operator locally conserves potential vorticity (PV). Mass and PV conservation is to machine precision, while energy conservation is to the level of time-truncation error and nonadiabatic processes in the advection of specific humidity. The energy dissipation introduced by these terms is less than 0.02 W m−2 (Taylor 2011).

Fig. 1.

An example quadrilateral element grid for the sphere. An inscribed cube is projected on the surface of the sphere. The faces of the cubed sphere are further subdivided to form a quadrilateral grid of the desired resolution. Coordinate lines from the gnomonic equal-angle projection are shown.

Fig. 1.

An example quadrilateral element grid for the sphere. An inscribed cube is projected on the surface of the sphere. The faces of the cubed sphere are further subdivided to form a quadrilateral grid of the desired resolution. Coordinate lines from the gnomonic equal-angle projection are shown.

We have compared the computational performance of CAM-SE, -FV, and -EUL at high resolution (0.25° and 0.125°) using the CCSM running in prescribed SST mode in Dennis et al. (2012). We summarize the 0.25° results in Fig. 2. The figure shows the atmosphere component times only so that we can directly compare the different dynamical core options. It ignores the cost of the other components, which contribute from 25% to 50% of the total cost of the CCSM. CAM-EUL remains the most efficient model at low processor counts, achieving 0.8 simulated years per day (SYPD) on only 2048 cores. But as the number of cores is increased, the performance of CAM-EUL plateaus at 0.87 SYPD. CAM-SE and CAM-FV are similar in performance low processor counts, but CAM-SE has near-perfect scalability to 86 400 cores, achieving a top speed of 12.2 SYPD, whereas CAM-FV is less scalable and achieves its best performance of 2.49 SYPD on 53 248 cores.

Fig. 2.

Performance of the CCSM atmosphere component model on Intrepid (IBM BG/P) when using the CAM-SE, -FV, or -EUL dynamical core, showing the simulated years per day (SYPD) as a function of the number of processing cores. Atmosphere component times taken from a CCSM time-slice simulation, coupling the atmosphere (at 0.25° or T341 resolution), the land model (0.25° resolution), and the sea ice and data ocean model (0.1°). The solid black line shows perfect parallel scalability. When using CAM-SE, the CCSM achieves near-perfect scalability down to one element per processor, running at 12.2 SYPD on 86 400 cores.

Fig. 2.

Performance of the CCSM atmosphere component model on Intrepid (IBM BG/P) when using the CAM-SE, -FV, or -EUL dynamical core, showing the simulated years per day (SYPD) as a function of the number of processing cores. Atmosphere component times taken from a CCSM time-slice simulation, coupling the atmosphere (at 0.25° or T341 resolution), the land model (0.25° resolution), and the sea ice and data ocean model (0.1°). The solid black line shows perfect parallel scalability. When using CAM-SE, the CCSM achieves near-perfect scalability down to one element per processor, running at 12.2 SYPD on 86 400 cores.

CAM-EUL uses a parallel strategy that makes use of multiple domain decompositions depending on the resolution and number of processors (Worley and Drake 2005). The column physics computations rely on a horizontal domain decomposition where each processor contains the entire vertical column of data for each horizontal grid point. The FFTs (in longitude) use a decomposition where each processor contains complete latitude bands, and the Legendre transforms (in latitude) use a decomposition where each processor contains complete longitude bands. At high processor counts, the communication to transpose between these different data decompositions eventually becomes the dominant cost of the model, causing the lack of scalability seen in Fig. 2. CAM-FV improves on the scalability of CAM-EUL because it does not require a data decomposition to support Legendre transforms, but it still requires decompositions to support the physics and the polar filter. CAM-SE uses a single decomposition across elements for both physics and dynamics. It thus requires no data-transpose operations to move data between multiple decompositions and instead relies solely on nearest-neighbor communication.

The parallel performance of CAM-SE also benefits from the spectral element Galerkin formulation (Dennis et al. 2012). The dynamics time step is implemented as a two-step process. Step 1 contains all numerical calculations and is completely local to each element. Step 2 is the application of the spectral element projection operator (equivalent to the traditional finite-element inverse-mass matrix). These two steps give a natural separation between computation and parallel communication. The step 1 computations are performed one element at a time and only require information stored at the Gauss–Lobatto nodes within each element. No interprocessor communication, ghost cell, or other neighbor information is needed. All communication is isolated to step 2, in which only element boundary data must be exchanged between adjacent elements. As all communication is isolated to a single projection operator, one need only focus on load-balancing strategies and message scheduling designed for this single operator. Significant resources have been devoted to optimizing this operator (Loft et al. 2001; Dennis 2003).

Performance benchmarks for an ultrahigh-resolution fully coupled CCSM, running a 0.125° atmosphere and 0.1° ocean, are given in Worley et al. (2011), where the CCSM obtains 2.6 SYPD using 204 408 cores. In that run, CAM-SE was the dominant component, using 172 800 cores running at 4.7 SYPD. For the moderate resolution (1°) Atmosphere Model Intercomparison Program (AMIP) configuration described below, we have made simulations on the Cray XT5 system at Oak Ridge National Laboratory. Using 912 cores (76 nodes), the CCSM obtains 16.5 SYPD, and the CAM-SE component represents 61% of the total cost, running at 27.2 SYPD. Within the atmosphere, the dynamics represents 72% of the total cost.

3. CCSM AMIP configuration

Most of the simulations presented here use the AMIP protocol (Gleckler 2004), running at approximately 1° resolution. We use the CCSM, version 4, coupling CAM with the 1° FV Community Land Model (CLM), the Community Ice Code (CICE) with prescribed ice extent, version 4, and a data ocean model that provides prescribed sea surface temperature (SST) data through the same coupler infrastructure as would be used by an active ocean model. The SST data are from the 1° Hadley dataset for time period 1979–2000 (Rayner et al. 2005). The CAM-FV simulations use a 0.9° × 1.25° latitude–longitude grid and are further described in Neale et al. (2011, manuscript submitted to J. Climate). CAM-SE uses a cubed-sphere grid where each cube face has 30 × 30 elements. The variables within each element are represented by polynomials up to degree 3, sampled on a 4 × 4 tensor product Gauss–Lobatto quadrature grid (Fig. 3). Counting all the nonoverlapping quadrature points of the functions within each element across all elements, the CAM-SE grid has an average grid spacing at the equator of 1° and a minimum grid spacing of 0.83°.

Fig. 3.

A 4 × 4 tensor product grid of Gauss–Lobatto nodes used within each element, for a degree d = 3 discretization. Nodes on the boundary are shared by neighboring elements.

Fig. 3.

A 4 × 4 tensor product grid of Gauss–Lobatto nodes used within each element, for a degree d = 3 discretization. Nodes on the boundary are shared by neighboring elements.

For this study, the CAM-SE AMIP simulation was configured to be as close as possible to CAM-FV. The main difference is that the CAM-SE simulations are performed with a tri-grid configuration (Craig et al. 2012). In a tri-grid configuration, the CCSM coupler is used to couple the atmosphere (running on the cubed sphere) with the CLM (running on a 0.9° × 1.25° latitude–longitude grid, also used by CAM-FV) and the data ocean model (running on a 1° CCSM ocean grid). Between these grids, the coupler uses conservative mapping weights generated by the SCRIP software package (Jones 1999). Thus, both CAM simulations use identical CLM configuration and SST datasets, but because of interpolation there will be slight differences in how the fluxes are represented on the atmosphere grid.

All of the simulations use the identical CAM, version 4, physics (Neale et al. 2010, 2011, manuscript submitted to J. Climate) with a 30-min physics time step and 26 vertical levels with a model top at 2.2 hPa. CAM-SE uses the default CAM-EUL T85 tunings, with the exception of low and high cloud relative humidity threshold parameters (rhminl and rhminh, respectively). These parameters have been determined so as to produce an energy-balanced simulation at the top of the atmosphere when running with 1850-like conditions. The globally averaged annual energy budgets are sensitive to these values (Williamson et al. 1995; Stratton 1999; Jackson et al. 2008) because they represent the minimum threshold for the formation of low and high clouds over a resolution-dependent gridbox area, and they must be chosen carefully. The values rhminl = 0.91 and rhminh = 0.78 were selected to produce a global balance of shortwave and longwave energy entering and exiting the atmosphere at the model top and surface. Also, they were set such that the zonally averaged levels of shortwave and longwave energy fluxes through the vertical model boundaries were very close to CAM-FV preindustrial simulations using default physics parameter settings relative to observations (not shown). For reference, the CAM-FV at 1° resolution uses rhminl = 0.92 and rhminh = 0.77.

With respect to the remaining tunable parameters, the only differences between CAM-SE and CAM-FV (due to the fact that the CAM-SE tunings were taken from the CAM-EUL default values) are in the cldwat_icritc, cldwat_icritw, zmconv_c0_lnd, and zmconv_c0_ocn parameters described in Neale et al. (2010). The values for CAM-SE were 16 × 10−6, 4 × 10−4, 0.004, and 0.004, while CAM-FV uses 18 × 10−6, 2 × 10−4, 0.0035, and 0.0035, respectively.

4. Grid imprinting

Grid imprinting is of special concern for methods on nonlatitude/longitude grids, as any such grid will have some anisotropy and must contain some special points. For the cubed-sphere grid, the main concern is anomalous forcing of an m = 4 mode caused by the eight special points at the cube corners. In addition, the use of Gauss–Lobatto nodes within each element (Fig. 3) is nonequally spaced.

For CAM-SE, this issue has been studied extensively. In Lauritzen et al. (2010), baroclinic instability triggered by grid anisotropy is compared across eight different dynamical cores, including cores running on cubed-sphere and icosahedral grids. Of the nonlatitude/longitude grids, CAM-SE shows the least amount of grid imprinting. A more stringent test looks at the climate in aquaplanet simulations with full physics. When run with zonally symmetric boundary conditions and forcing, any grid anisotropy would be expected to show up in long time averages where all transient flow features have been averaged out. In Taylor et al. (2008), the time-averaged vertical pressure velocity (one of the noisiest fields) is shown to have no visible grid imprinting. It does show some departures from zonal symmetry, but these are at the same level as in the (perfectly isotropic) CAM-EUL model.

We attribute CAM-SE’s low levels of grid imprinting to the use of relatively high-order numerics and the fact that finite element methods have a long history of dealing with grids far more unstructured and anisotropic than the cubed sphere. With respect to the quadrature nodes, we note that their use is similar to the quadrature grid used in CAM-EUL: they are used to evaluate the integrals that appear in Galerkin methods, but the underlying representation (polynomials in the case of CAM-SE and spherical harmonics in the case of CAM-EUL) does not contain the nonuniformities seen in the quadrature points.

5. Kinetic energy spectra

A comparison of the horizontal kinetic energy spectra among the CAM dynamical cores is one way to quantify solution accuracy and characterize the dissipation properties of the dynamical core (Skamarock 2004, 2011). We compute the spectra from global 250-hPa velocity u snapshots taken every 6 days, via a vector spherical harmonic transform (Adams and Swarztrauber 1997). For CAM-SE, the data are first interpolated from the cubed-sphere grid to a latitude–longitude grid using the element shape functions within each element. For vectors, we interpolate their components expressed in the gnomonic contravariant coordinate system and then map the result to spherical coordinates. This avoids the interpolation issues that arise when trying to interpolate individual latitude and longitude components, which are discontinuous at the poles. Given a vector spherical harmonic expansion in harmonics of degree k and mode m, we consider the usual spectra E(k) giving the energy in the harmonics of degree k, summed over m. At large scales, the atmosphere behaves as a quasi-two-dimensional flow with a strong enstrophy cascade, resulting in a −3 scaling, E(k) ~ k−3, matching observations (Nastrom and Gage 1985; Lindborg 1999). At smaller scales, below several hundred kilometers, the atmosphere has a robust transition into a −5/3 regime, which is less well understood. For global models, this Nastrom–Gage transition is only captured at very high resolutions, requiring O(10 km) grid spacing and a low dissipation numerical method (Hamilton et al. 2008).

a. Moderate-resolution spectra

In Figs. 4 and 5 we show the spectra from AMIP simulations with approximately 1° resolution. The spectra is computed from 1 month of instantaneous flow snapshots (five snapshots, every 6 days) and then averaged. We plot the spectra for (solid lines) and the divergent (irrotational) component (dotted lines). The divergent component is defined via the Helmholtz decomposition, with and . At these scales, almost all the energy is contained in the rotational (solenoidal) component , but it is illustrative to look at the divergent component separately. All three models approach the −3 scaling. The differences between the models are more easily seen in Fig. 5, which plots k3E(k) so that the −3 scaling is represented by a horizontal line. One can see that CAM-EUL is by far the least dissipative model, capturing the −3 scaling for almost all resolved scales. CAM-SE is closer in character to CAM-EUL than to CAM-FV, showing good agreement with CAM-EUL for most wavenumbers and only departing from CAM-EUL as the resolution approaches the truncation limit. The results for CAM-FV and CAM-EUL are consistent with that seen in idealized aqua planet simulations (Jablonowski and Williamson 2011). CAM-FV departs from the −3 scaling at relatively low wavenumbers. With respect to the divergent component, CAM-SE and CAM-EUL are very similar, while the CAM-FV spectra show the impact of its use of a second-order divergence damping (Lauritzen et al. 2012) starting around wavenumber 15. We expect that with the more scale-selective fourth-order divergence damping used in the cubed-sphere FV core (Donner et al. 2011), CAM-FV would behave more like CAM-EUL and CAM-SE, as the latter two models both rely on a fourth-order hyperviscosity operator.

Fig. 4.

The kinetic energy spectra from CAM-SE, CAM-FV, and CAM-EUL at about 1° resolution.

Fig. 4.

The kinetic energy spectra from CAM-SE, CAM-FV, and CAM-EUL at about 1° resolution.

Fig. 5.

As in Fig. 4, but plotting k3E(k) to better illustrate how the spectra matches the predicted k−3 scaling (black line). Solid lines show the kinetic energy of u, and dotted lines show the divergent component .

Fig. 5.

As in Fig. 4, but plotting k3E(k) to better illustrate how the spectra matches the predicted k−3 scaling (black line). Solid lines show the kinetic energy of u, and dotted lines show the divergent component .

b. High-resolution spectra

We also show the spectra from high-resolution (0.25° and 0.125°) aquaplanet simulations (Neale and Hoskins 2000a,b) in Figs. 6 and 7, averaged over 1 yr of data (72 snapshots, taken every 5 days) using the CAM as configured in Williamson (2008a,b). Averaging over 72 snapshots has eliminated much of the noise that was present in the low-resolution AMIP spectra in Fig. 4. Although these data are from aquaplanet simulations, preliminary results indicate that the spectra from high-resolution AMIP simulations will be quite similar. In the low-resolution results, the CAM-SE spectra rolled off earlier than the CAM-EUL spectra, but in the high-resolution case, the figure shows that the CAM-SE 0.25° and CAM-EUL T341 simulations are quite similar, and agree well up to the maximum wavenumber resolved by the T341 simulation. We note that the T341 simulation uses a grid of size 512 × 1024 with an equatorial grid spacing of 0.35°. At this resolution there is some hint of the Nastrom–Gage −3 to −5/3 transition, but it is not fully resolved until the resolution is increased to 0.125°. The CAM-SE 0.125° simulation has both a −3 regime as well as fully resolved −5/3 regime, best seen in Fig. 7. We expect that CAM-EUL at T720 would obtain a similar result. However, in the −5/3 regime, one can see that the magnitude of the divergent component is now significant (in Fig. 7, with a value of 30 out of a total of 80). Resolving this component of the energy is a requirement for capturing the Nastrom–Gage transition, suggesting that the second-order divergence damping would not be appropriate at these resolutions.

Fig. 6.

The kinetic energy spectra from high-resolution aquaplanet simulations of CAM-SE and CAM-EUL.

Fig. 6.

The kinetic energy spectra from high-resolution aquaplanet simulations of CAM-SE and CAM-EUL.

Fig. 7.

As in Fig. 6, only plotting k5/3E(k) to better illustrate how the spectra matches the predicted k−3 and k−5/3 scalings (black lines). Solid lines show the kinetic energy of u, and the dotted lines show the divergent component . Only the highest resolution, CAM-SE at 0.125°, has regions matching both scaling regimes.

Fig. 7.

As in Fig. 6, only plotting k5/3E(k) to better illustrate how the spectra matches the predicted k−3 and k−5/3 scalings (black lines). Solid lines show the kinetic energy of u, and the dotted lines show the divergent component . Only the highest resolution, CAM-SE at 0.125°, has regions matching both scaling regimes.

6. Mean climate

We now turn to the mean climate (1981–2000) of CAM-SE and CAM-FV 1° resolution AMIP simulations. The data presented in this section are computed from the model output by the publicly released CAM Atmosphere Model Working Group diagnostics package. The package computes an overall error measure from the Taylor diagram (Taylor 2001) from 10 key diagnostics (including sea level pressure, cloud forcing, rainfall, temperature, wind stress, zonal wind, and relative humidity) and normalized by the results from the previous CAM, version 3.5. The root-mean-square error (RMSE), not including the bias, is 0.920 for CAM-SE and 0.937 for CAM-FV, showing that CAM, version 4, represents an 8% improvement in RMSE over version 3.5, and CAM-SE obtains a slight improvement over CAM-FV. Similar results are obtained for the bias, where CAM-SE and CAM-FV have biases of 0.839 and 0.905, respectively.

We present global annually averaged values of some key variables and corresponding observed values in Table 1. The variables RESTOM, FSNT(TOA), CLDTOT, CLDHGH, CLDLOW, SWCF, and LWCF refer to the residual energy flux at the model top, the net absorbed shortwave energy at the top of the atmosphere, the fractional coverage of total, high, and low clouds, and the shortwave and longwave cloud forcing, respectively. The variables TS and U200 hPa refer to the global annually averaged surface temperature and the annually averaged 200-hPa zonal wind field for the duration of the AMIP run. Observational values used for comparison come from the following datasets: Clouds and the Earth’s Radiant Energy System (CERES; Loeb et al. 2009) for FNST(TOA), LWCF, and SWCF; the National Centers for Environmental Prediction (NCEP) reanalysis (Kalnay et al. 1996; Kistler et al. 2001) for the surface temperature and 200-hPa zonal wind; and International Satellite Cloud Climatology Project (ISCCP) D2 (Rossow and Schiffer 1999) for the cloud (CLDTOT, CLDHGH, and CLDLOW) fields.

Table 1.

Global annually averaged values of key atmospheric variables that govern energy balance for 1°CAM-SE and CAM-FV simulations, along with observed quantities (OBS). See text for explanation of variables. Units are W m−2 except for TS (K) and U200 hPa (m s−1).

Global annually averaged values of key atmospheric variables that govern energy balance for 1°CAM-SE and CAM-FV simulations, along with observed quantities (OBS). See text for explanation of variables. Units are W m−2 except for TS (K) and U200 hPa (m s−1).
Global annually averaged values of key atmospheric variables that govern energy balance for 1°CAM-SE and CAM-FV simulations, along with observed quantities (OBS). See text for explanation of variables. Units are W m−2 except for TS (K) and U200 hPa (m s−1).

Overall, the simulations produce a similar global climate, relative to observations. The RESTOM for both models are within the 1.1 ± 0.4 W m−2 estimate from a collection of observations of the earth’s energy balance at the top of the atmosphere from 1970 to 2000 (Murphy et al. 2009). For five of the nine variables listed in Table 1, the two models produce global annually averaged values closer to each other than observations. Note that due to overlap and a separate accounting of midlevel clouds, the high and low clouds to not sum up to CLDTOT.

As presented in Table 1, the dynamically based prognostic variables in CAM-SE such as temperature and wind speed match very closely to CAM-FV as well as observations. Figure 8 shows the annually averaged sea level pressure (SLP) values for CAM-SE and CAM-FV covering the AMIP period, and the overall distribution including the robust minima over the North Pacific and North Atlantic is captured well. The North Pacific low is more robust with CAM-SE than CAM-FV and observations, but its overall Arctic pressure minima are slightly closer to observations. The global horizontal distribution of annually averaged SLP in CAM-SE has a mean value of 1011.12 hPa, compared to 1011.25 hPa for FV and 1011.62 hPa from the NCEP reanalysis.

Fig. 8.

Annually averaged sea level pressure for CAM-SE, CAM-FV, and NCEP reanalysis.

Fig. 8.

Annually averaged sea level pressure for CAM-SE, CAM-FV, and NCEP reanalysis.

One robust example of the similarity of CAM-SE and CAM-FV is the total annual implied northward ocean heat transport. Figure 9 shows that as observed, most of the transport occurs in the tropical regions. Both models produce transport values very close to each other and at levels near the lower edge of the error of the estimate (Trenberth and Caron 2001).

Fig. 9.

Annual implied northward ocean heat transport (PW) of the total ocean for the CAM-SE and -FV AMIP runs compared to the NCEP-derived data (Trenberth and Caron 2001).

Fig. 9.

Annual implied northward ocean heat transport (PW) of the total ocean for the CAM-SE and -FV AMIP runs compared to the NCEP-derived data (Trenberth and Caron 2001).

The statistics of the hydrological cycle within CAM-SE and CAM-FV are quite similar. The precipitation rate is 3.0 mm day−1 with CAM-SE and 2.9 mm day−1 with CAM-FV, compared to a global annual average of 2.6 mm day−1 from Global Precipitation Climatology Project (GPCP) data (Adler et al. 2003). GPCP precipitation is the most complete precipitation dataset, particularly over the oceans. It is a merged product of satellite, gauge, and sounding data and is the most relevant dataset choice for lower-resolution global climate model studies. Figure 10 shows that the models are much closer to each other than to the observations. The RMSE between the two models is 0.55, while their RMSE with respect to observations is 1.15 and 1.13 for CAM-SE and CAM-FV, respectively. They both significantly overestimate the average maximum precipitation rates in the tropics (a more significant analysis is given in section 7). The difference plots in Fig. 11 show that regionally there are significant biases in both models over most of the Pacific ITCZ, the western and eastern coasts of India, and over the tropical warm pool over the western Pacific. There are several localized biases in the CAM-SE simulation over the tropical Pacific warm pool, specifically near Jakarta, Indonesia, Papua New Guinea, and western Colombia. There are also several regions where the biases are lower with SE than FV, namely off the western and eastern coasts of India. These relative model biases are within regions of strong overall precipitation biases that reach about 6 mm day−1.

Fig. 10.

Precipitation rate from CAM-SE, CAM-FV, and GPCP.

Fig. 10.

Precipitation rate from CAM-SE, CAM-FV, and GPCP.

Fig. 11.

Precipitation rate difference plots between CAM-SE and CAM-FV, and between CAM-SE and GPCP.

Fig. 11.

Precipitation rate difference plots between CAM-SE and CAM-FV, and between CAM-SE and GPCP.

The model-produced spurious precipitation features near the Tibetan plateau (visible in Fig. 11) are also common to past versions of CAM. Alternative precipitation datasets including the Climate Prediction Center (CPC) Merged Analysis of Precipitation (CMAP; a merged satellite-only product) and Tropical Rainfall Measuring Mission (TRMM)-3B42 (a merged satellite whose native resolution is 25 km) show similar observed features in this region. So this precipitation bias remains a distinct CAM problem related to insufficient blocking effects from steep orography when using such low horizontal resolutions. Addressing these problems at these resolutions is an active area of research and is expected to involve more accurately representing blocked flows and form drag due to unresolved subgrid-scale orographic features.

The annually averaged zonally averaged zonal wind fields with CAM-SE show close agreement with CAM-FV compared to NCEP observations. We display the seasonally averaged zonal wind fields (Figs. 12 and 13) because the polar winter jet stream governs many important aspects of global climate, including the meridional transport of heat, the frequency and location of storm tracks, and the global distribution of surface pressure and temperature. Figure 12 shows the zonally averaged zonal wind field averaged over December–February (DJF) for CAM-SE, CAM-FV, and NCEP observed values covering the AMIP period. Both CAM-SE and CAM-FV overestimate the easterly flow near the equator; however, the CAM-SE is able to represent the stratospheric Arctic winter jet better than FV, which is too strong by about 9 m s−1. The stratospheric tropical easterlies are also overestimated by both models in the June–August (JJA) season, as seen in Fig. 13.

Fig. 12.

Zonally averaged zonal wind for DJF from CAM-SE, CAM-FV, and NCEP.

Fig. 12.

Zonally averaged zonal wind for DJF from CAM-SE, CAM-FV, and NCEP.

Fig. 13.

Zonally averaged zonal wind for JJA from CAM-SE, CAM-FV, and NCEP.

Fig. 13.

Zonally averaged zonal wind for JJA from CAM-SE, CAM-FV, and NCEP.

The annually averaged horizontal distributions of the zonal wind field at 200 hPa, where the tropospheric jets reach maximum amplitude, are displayed in Fig. 14 for both models and NCEP observations. Unlike Figs. 12 and 13, which show the seasonal averages, Fig. 14 shows the annually averaged values and thus highlights more general behavior of the winds. The RMSE between the two models for this field is 1.32, which is less than half the RMSE of the models compared to NCEP observations, which are 2.87 and 2.52 for CAM-SE and CAM-FV respectively. The difference plot (not shown) indicates that the higher differences of CAM-SE are due to the overestimation of the Southern Hemisphere tropospheric jet. This is consistent with the surface wind stress in the same location (as in Fig. 16). CAM-FV is slightly closer to observations at 200 hPa, although the differences between the models are small relative to the uncertainty of the observations. Both models are also a significant improvement over version 3 of CAM, which was not able to capture the structure of the observed jets with as much fidelity (Hurrell et al. 2006). Other improvements in CAM from version 3 to 4 are documented in Gent et al. (2011).

Fig. 14.

Zonal wind at 200 hPa for CAM-SE, CAM-FV, and NCEP.

Fig. 14.

Zonal wind at 200 hPa for CAM-SE, CAM-FV, and NCEP.

Figure 15 shows the annual zonally averaged vertical pressure velocities for CAM-SE, CAM-FV, and NCEP observations. This field is sensitive to the smoothness of the topography datasets. The surface topography is necessarily represented as an approximation to the observed topography, and the roughness of this field impacts the diagnosed vertical pressure velocity. At present, CAM-SE uses a smoother topography dataset in order to reduce the level of noise in the vertical velocity, as can be seen in the figure. To compare the amount of orographic smoothing across dynamical cores, we look at the E(k) of the height field, where E(k) is defined as in section 5. We define the resolved wavenumber as the value of k where the smoothing has reduced E(k) by 50% from its original unsmoothed value. By this measure, CAM-FV has the roughest topography, resolving k < 71, while CAM-EUL and CAM-SE use significantly smoother topography, with k < 40 and k < 33, respectively. In the future we plan on using an improved remapping algorithm to generate topography datasets tailored for CAM-SE and with less smoothing.

Fig. 15.

Zonally averaged vertical velocity for CAM-SE, CAM-FV, and NCEP.

Fig. 15.

Zonally averaged vertical velocity for CAM-SE, CAM-FV, and NCEP.

Both CAM-SE and CAM-FV match observed pressure vertical velocity through most of the atmosphere, but significantly overestimate (more negative) the upward motion at the ITCZ. From the difference plot between CAM-FV and CAM-SE (not shown), CAM-FV is about 3 hPa day−1 more negative than CAM-SE throughout the ITCZ. This quantity is an important measure of the vertical transport of many thermodynamic quantities that determine cloud formation and precipitation. Unfortunately, the reduced bias in CAM-SE is not translated into a more significant improvement in the simulated precipitation.

The surface wind stress over the ocean is an important momentum driver for the ocean from the atmosphere. The two models are globally 0.01 N m−2 apart and slightly closer to each other than values estimated from the European Remote Sensing Satellite scatterometer data (Stoffelen and Anderson 1997a,b), as shown in Fig. 16. Both models overestimate the wind stress around the Southern Hemisphere midlatitudes and to a lesser degree the North Atlantic storm tracks, an issue that has been present in the CAM, version 3, where it is attributed to underestimated gravity wave drag in the mountain stress contribution to the balanced atmospheric momentum flux (Collins et al. 2006). CAM-SE values are higher than CAM-FV and are significantly further from observations in that region, suggesting that the gravity wave drag is too weak in CAM-SE, due to CAM-SE’s use of smoother topography.

Fig. 16.

Surface wind stress for CAM-SE, CAM-FV, and NCEP.

Fig. 16.

Surface wind stress for CAM-SE, CAM-FV, and NCEP.

Considering some of the polar climate features described above, such as the Northern Hemisphere sea level pressure (Fig. 8), the Southern Hemisphere surface wind stress over the ocean (Fig. 16), and the stratospheric jets (Figs. 12 and 13), we note that there does not appear to be any significant improvement due to CAM-SE’s lack of a polar filter. CAM-SE and CAM-FV have very similar biases in sea level pressure, with the CAM-SE bias slightly worse in the North Pacific. Similarly for the Southern Hemisphere wind stress, CAM-SE and CAM-FV both have a large bias that is slightly larger in CAM-SE. The Northern Hemisphere polar night jet is improved in CAM-SE, but experiments show this is due not to the lack of a polar filter but to the top-of-model dissipation used by CAM-SE.

7. Transient features

The mean climate presented in the preceding section is composed of transient features that span a wide range of space and time scales. Although differences in dynamical cores are not apparent in the mean simulation they may be more apparent in transient statistics due to differences seen at the smallest scales in the KE spectra plots. In this section we assess some of these transient features in CAM-SE and CAM-FV as compared to observations. We focus on the seasonal migration of the intertropical convergence zone (ITCZ) and zonal propagation. These features are especially important in the tropical belt and regulate most of the tropical climate variability, but they are difficult to simulate satisfactorily (Gates et al. 1999; Hack et al. 1998; Hurrell et al. 2006; Lin et al. 2006; Wu et al. 2003).

a. Meridional migration of the ITCZ

In Fig. 17, the climatology (1981–2000) of zonal mean precipitation is shown from GPCP observations, CAM-SE, and FV. The top row includes all longitudes in the mean. Observations [Fig. 17a(1)] show that the peak of the ITCZ migrates from south to north of the equator from about January to July and then migrates southward from about August to December. The peak is situated at around 8°S and 8°N in January and July, respectively. The ITCZ covers a latitudinal belt of about 20° and extends up to 20°S and 20°N in January and July, respectively. A notable feature is that its northward migration is comparatively slower than the southward retreat; it takes 7–8 months going north and only 4–5 months going south. Also, the intensity of the ITCZ is greater in the Northern Hemisphere during boreal summer. The average precipitation at the peaks is on the order of 10 mm day−1 in the Northern Hemisphere. Inspection of the ITCZ in CAM-SE [Fig. 17b(1)] indicates that the broad features are largely captured by the model. The peak occurs at around 8°S in January, migrates northward until July, and then proceeds to return south. The Northern Hemisphere has a greater intensity as observed and the southward progression is faster than the northward as in the observations. The shortcomings include an overestimation of the intensity, especially in the Northern Hemisphere, and a secondary ITCZ at around 5°N during January–April that is manifested in the form of stationary rainfall belts at around 5°–8°N that persist all year. The latitudinal spread of the ITCZ is 30°–40°, which is wider than observations. It is noted (not shown here) that the overestimation in intensity during boreal summer is primarily over the Bay of Bengal, central Pacific, western coast of Mexico, and Panama regions. The spurious ITCZ during boreal winter exists over the Indian Ocean and western Pacific. The excess latitudinal extent is due to spurious rainfall over the Tibetan Plateau and South Pacific convergence zone during boreal summer. Figure 17c(1) shows the same zonal mean precipitation from CAM-FV, and displays similar biases.

Fig. 17.

Mean precipitation from (a1),(a2) GPCP observations; (b1),(b2) CAM-SE; and (c1),(c2) CAM-FV. Zonally averaged (top) over the globe and (bottom) over 60°–90°E.

Fig. 17.

Mean precipitation from (a1),(a2) GPCP observations; (b1),(b2) CAM-SE; and (c1),(c2) CAM-FV. Zonally averaged (top) over the globe and (bottom) over 60°–90°E.

Because the earth’s surface has zonal asymmetry, characteristics of the ITCZ vary regionally. For instance, behavior over the Indian region is different from that over African and American regions (Srinivasan and Smith 1996). Therefore, regional zonally averaged precipitation is also examined. The bottom row of Fig. 17 shows the meridional migration for the Indian longitudes (60°–90°E) from observations, CAM-SE, and CAM-FV. Over this region, there are two ITCZs, one around 5°S year-round and another around 20°N during the South Asian monsoon (June–September). The secondary ITCZ develops abruptly over 5°S in April, moves northward, and reaches 20°N and then moves southward in August and September. The primary ITCZ is situated over the Indian Ocean, whereas the secondary occurs over the Indian subcontinent. CAM-SE captures the primary aspects of the regional ITCZ such as the double peaks and seasonal migration; however, a spurious ITCZ is simulated over 0°–10°N during January–March, the secondary peak over the Indian subcontinent is overestimated, and spurious rainfall around 30°N is simulated by the model. In the spatial distribution of precipitation (Fig. 10), the model simulates excessive rainfall north of the equatorial eastern Arabian Sea during January–March, which is manifested as the spurious ITCZ during the same time over 0°–10°N The spurious rainfall around 30°N is due to the excessive rainfall over the Himalayas during the South Asian monsoon.

In general, CAM-SE captures the broad features although significant biases present in CAM-FV persist in SE. Some of these shortcomings are long-standing issues in climate modeling (Hack et al. 1998; Gates et al. 1999) and are associated with the physics parameterization (Wu et al. 2003). The ITCZ precipitation is a result of nonlinear interaction among dynamic, thermodynamic, and physical processes, and imperfections in any of them could lead to shortcomings in simulating this phenomenon.

b. Zonal propagation

In the tropics, especially over the equatorial belt, convection occurs at various spatial and temporal scales and propagates primarily in the zonal direction. Within convective systems, cloud clusters interact to produce a hierarchy of collective motions and give rise to convectively coupled equatorial waves (CCEWs) that control a substantial fraction of tropical variability. The scales of these waves in the simulations are examined using the methodology of Wheeler and Kiladis (1999). Figures 18 and 19 show symmetric and antisymmetric components of the normalized power spectra of the outgoing longwave radiation (OLR) averaged from 15°S to 15°N from CAM-SE, CAM-FV, and observations (Liebmann and Smith 1996). This normalization procedure removes a large portion of the systematic biases within the models and more clearly displays the model disturbances with respect to their own climatological variances at each scale. The regions of wavenumber–frequency space defining the (meridional mode n = −1) Kelvin, n = 1 equatorial Rossby (ER), n = 0 mixed Rossby–gravity (MRG), n = 0 eastward inertio-gravity (EIG), n = 1 westward inertio-gravity (n = 1 WIG), n = 2 westward inertio-gravity (n = 2 WIG), and Madden–Julian oscillation (MJO) modes are similar to Wheeler and Kiladis (1999). The conventional dispersion curves of shallow water modes for equivalent depths of 12, 25, and 50 m are shown in the figures.

Fig. 18.

Wheeler–Kiladis diagrams showing the OLR power spectra (symmetric components) for (a) observations, (b) CAM-SE, and (c) CAM-FV.

Fig. 18.

Wheeler–Kiladis diagrams showing the OLR power spectra (symmetric components) for (a) observations, (b) CAM-SE, and (c) CAM-FV.

Fig. 19.

As in Fig. 18, but only showing the antisymmetric components.

Fig. 19.

As in Fig. 18, but only showing the antisymmetric components.

These waves are readily identified in the observational spectra and, as in Wheeler and Kiladis (1999), the spectral peaks match best with an equivalent depth of around 25 m. Some of these modes are captured well by the models, particularly the Kelvin, ER, and MRG waves and the MJO. The two models show similar patterns, namely prominent Kelvin, ER, and MRG waves, and weak WIG and EIG waves and MJO. However, there are some shortcomings in the simulations: weak Kelvin, WIG, and EIG waves and MJO and some differences between the two simulations. In the models, the Kelvin waves have most of their variance centers around 50-m equivalent depth at lower wavenumbers and centers around 25-m equivalent depth at higher wavenumbers, which corresponds to 22.1 and 15.6 m s−1, respectively, as seen in the observations. There is an increase in the speed of Kelvin waves at smaller scales. However, there is a lack of power in Kelvin modes, especially at higher wavenumbers (above 4). The models simulate spurious variances at wavenumber 1 and periods of 20–30 days. The variance in FV is marginally greater, although the scales of the Kelvin waves are found to be largely similar in both the models. The MJO is the other eastward-propagating mode with periods of 30–70 days and wavenumbers 1–5. The symmetric component of the MJO is seen in Fig. 18. Both the models show some variance within these bands. The symmetric component of the westward-propagating disturbances in the wavenumber range of 1–10 and the period from 10 to 20 days is the ER. It is seen from Fig. 18 that the models satisfactorily capture these waves, except an overestimation of variances around wavenumbers 2–4 and the 60–80-day period. It appears that the models simulate some kind of stationary waves with scales similar to MJO. The n = 1 WIG is another symmetric component of the westward-propagating waves with less than a 2.5-day time scale. In this regime, the variance is too weak in the models. Figure 19 shows the antisymmetric waves. The variance in the MRG waves is captured well by the models. However, in the EIG regime, the variances are feeble, and phase speeds are too slow, scaled to shallow equivalent depths. The n = 2 WIG is also weak in both models (not shown).

8. Regional climate: South Asian monsoon

Another important evaluation of CAM-SE is the ability to simulate the regional aspects of climate, particularly the remarkable South Asian monsoon. The South Asian monsoon occurs from June through September. Figure 20 shows observed June–September (JJAS) averaged rainfall [Fig. 20a(1)] and 850-hPa wind climatology [Fig. 20a(2)] in the vicinity of the South Asian monsoon region. The climatology is based on GPCP rainfall data from 1979 to 2000 and 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40) data for 850-hPa wind. Some of the notable features of South Asian monsoon seen in the figure are the occurrence of maximum rainfall over the head of the Bay of Bengal, the extension up to an area south of the equator between 80° and 100°E, and a secondary maximum over the western coast of India. In the vicinity of the South Asian monsoon region and during the same period, there is substantial rainfall over the western Pacific and almost no rainfall over Saudi Arabia. A cross-equatorial flow and southern equatorial easterlies exist in the lower troposphere [Fig. 20a(2)]. The Somali jet passes over the Indian Peninsula and penetrates up to around 120°E (i.e., into the western Pacific).

Fig. 20.

Contour plots of mean simulated (a1),(b1),(c1) rainfall and (a2),(b2),(c2) wind over the Indian Ocean, from (top) observations, (middle) CAM-SE, and (bottom) CAM-FV. The CAM-SE and CAM-FV pattern correlation coefficient (PCC) with observations is also given.

Fig. 20.

Contour plots of mean simulated (a1),(b1),(c1) rainfall and (a2),(b2),(c2) wind over the Indian Ocean, from (top) observations, (middle) CAM-SE, and (bottom) CAM-FV. The CAM-SE and CAM-FV pattern correlation coefficient (PCC) with observations is also given.

Figures 20b(1),b(2) show the simulated rainfall and wind over the same region at 850 hPa. The model is able to capture some of the features (e.g., rainfall over Bay of Bengal, the Indian subcontinent, and the Somali jet). Shortcomings include overestimated rainfall over the Bay of Bengal, the western coast of India, the western equatorial Indian Ocean, and the Himalayas and underestimated rainfall over the eastern equatorial Indian Ocean (western coast of the Maritime Continent). Both CAM-SE and CAM-FV simulate unrealistic heavy rainfall over Saudi Arabia and an overly strong simulated Somali jet. The pattern correlation between observed and simulated rainfall with CAM-SE and CAM-FV over the region between 40° and 120°E and between 20°S and 40°N is 0.59 and 0.89, respectively [see top of Figs. 20c(1),c(2)]. It is notable that the correlation coefficient of rainfall and wind is improved to 0.68 and 0.94, respectively, with CAM-SE [see top of Figs. 2b(1),b(2)]. The ITCZ has become more realistic, and the biases over the Himalayas have been mitigated to some extent, which can be attributed to smoother orography in SE. The dry bias over the equatorial western Indian Ocean is also less severe. The low-level southwesterly jet is more realistic in CAM-SE.

Figure 21 shows the meridional circulation over the South Asian monsoon region and, in particular, a strong ascent over the Indian subcontinent accompanied with strong descent over the southern Indian Ocean and low-level inflow toward the land surface and upper-level outflow toward the Indian Ocean. These form the regional Hadley cell, the broad features of which the CAM-SE and CAM-FV models largely capture although the circulation strength is overestimated. This is associated with an overestimation of the precipitation over the Indian subcontinent and the Bay of Bengal. Another shortcoming of the models is that the precipitation is overestimated over the Himalayas, which is due to the fact that they simulate overly strong ascending motion over the Tibetan plateau (however, the ascent over the Himalayas in the lower troposphere is a plotting artifact caused by extrapolating the winds to pressures exceeding the local surface pressure). The presence of the biases in both models again suggests that they may be related to deficiencies in the physics parameterizations.

Fig. 21.

Time (JJAS)-mean zonally (60°–120°E) averaged meridional circulation from (a) observations, (b) CAM-SE, and (c) CAM-FV.

Fig. 21.

Time (JJAS)-mean zonally (60°–120°E) averaged meridional circulation from (a) observations, (b) CAM-SE, and (c) CAM-FV.

9. Conclusions

CAM-SE represents the successful integration of an unstructured grid spectral finite-element dynamical core into the CAM. Despite the large numerical differences between the spectral element and finite-volume dynamical cores in CAM, the climates produced by the models agree remarkably well over a wide range of means and transient features. CAM-SE and CAM-FV each have strengths and weaknesses when compared to observations, but these differences are small when compared to the overall biases present in both models, as expected, due to the many parameterized physical processes in CAM. CAM-SE provides increased scalability at high resolution, obtaining excellent simulation rates at both 0.25° and 0.125° resolution. CAM-SE’s high-order accuracy and low dissipation allows it to fully capture the Nastrom–Gage transition in the KE spectra at 0.125° resolution. The scientific and performance results give us confidence that CAM-SE is an effective approach for developing a high-resolution capability within the CCSM.

Acknowledgments

The authors are grateful to Jim Hack for his assistance in tuning CAM-SE for energy balance and Nigel Wood for many constructive comments. We also acknowledge the CAM4 developers, including but not limited to members of the Atmospheric Model Working Group. Members of the Software Engineering Working Group were instrumental in the integration of HOMME into the CAM. The CCSM project is supported by the National Science Foundation and the Office of Science (BER) of the U.S. Department of Energy (DOE). K.E. and M.T. were supported by the DOE BER SciDAC Grant 06-13194. This research used the Oak Ridge Leadership Computing Facilities at the Oak Ridge National Laboratory, supported by the Office of Science of the U.S. DOE under Contract DE-AC05-00OR22725, the Argonne Leadership Computing Facility at Argonne National Laboratory, supported by the Office of Science of the U.S. DOE under Contract DE-AC02-06CH11357, and Sandia National Laboratories facilities, managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. DOE National Nuclear Security Administration under Contract DE-AC04-94AL85000.

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Footnotes

*

Current affiliation: Indian Institute of Technology Delhi, New Delhi, India.

This article is included in the CCSM4 Special Collection.