Abstract

This study compares the error characteristics associated with two grid refinement approaches including global variable resolution and nesting for high-resolution regional climate modeling. The global variable-resolution model, Model for Prediction Across Scales-Atmosphere (MPAS-A), and the limited-area model, Weather Research and Forecasting Model (WRF), are compared in an idealized aquaplanet context. For MPAS-A, simulations have been performed with a quasi-uniform-resolution global domain at coarse (1°) and high (0.25°) resolution, and a variable-resolution domain with a high-resolution region at 0.25° configured inside a coarse-resolution global domain at 1° resolution. Similarly, WRF has been configured to run on a coarse (1°) and high (0.25°) tropical channel domain as well as a nested domain with a high-resolution region at 0.25° nested two-way inside the coarse-resolution (1°) tropical channel. The variable-resolution or nested simulations are compared against the high-resolution simulations. Both models respond to increased resolution with enhanced precipitation and significant reduction in the ratio of convective to nonconvective precipitation. The limited-area grid refinement induces zonal asymmetry in precipitation (heating), accompanied by zonal anomalous Walker-like circulations and standing Rossby wave signals. Within the high-resolution limited area, the zonal distribution of precipitation is affected by advection in MPAS-A and by the nesting strategy in WRF. In both models, the propagation characteristics of equatorial waves are not significantly affected by the variations in resolution.

1. Introduction

Global climate models (GCMs) have played a central role in the investigation of natural variability and anthropogenic forcing and response in the climate system. Despite some degree of robustness in projecting future changes in the global hydrological cycle (Held and Soden 2006), regional-scale responses remain highly uncertain due partly to the spatial resolution of the GCMs (Déqué 2000), which is limited to about 100 km or coarser because of computational resources. This gap in modeling capability has traditionally been filled by regional models forced offline by a global reanalysis or an independently run low-resolution global model (Giorgi 1990). This one-way nested grid refinement approach for regional climate modeling has since been used in numerous studies of land use (e.g., Pielke et al. 1992) and climate change (e.g., Caya and Laprise 1999; Leung et al. 2004), as well as studies of regional climate processes (Juang and Kanamitsu 1994; Leung et al. 2003; Leung and Qian 2003) and development and evaluation of physics parameterizations for GCMs (e.g., Leung and Ghan 1998; Ghan et al. 1999). Two-way nesting of global and regional climate models has also been attempted, and the limited results suggest the importance of upscaled or remote influence from the high-resolution regional simulation on the large-scale circulation of the global models (Lorenz and Jacob 2005; Inatsu and Kimoto 2009).

Besides nested modeling, several groups have developed and applied stretched grid methods to GCMs and used them in climate process studies or to project future climate changes. Fox-Rabinovitz et al. (2001) used a stretched grid version of the National Aeronautics and Space Administration (NASA) Goddard Earth Observing System GCM (GEOS SG-GCM) with a refined mesh over North America to simulate the anomalous 1988 U.S. summer drought. Lorant and Royer (2001) used a stretched grid version of the climate Action de Recherche Petite Échelle Grande Échelle (ARPEGE-Climat) GCM developed jointly by Météo-France and the European Centre for Medium-Range Weather Forecasts (ECMWF) and showed that changes in grid resolution over the stretched grid interact with physics to introduce zonally nonuniform features in aquaplanet simulations. Furthermore they found that variations in spatial resolutions affect the propagation of equatorial waves. Nevertheless stretched grid models have been applied in studies involving real-world simulations such as African easterly waves (Moustaoui et al. 2002), the Asian monsoon (Zhou and Li 2002; Nguyen and McGregor 2009), climate change over the Mediterranean region (Gibelin and Déqué 2002) and Africa (Maynard and Royer 2004), as well as the effect of global warming on hurricanes (Chauvin et al. 2006).

More recently, global models with local grid refinement have also become available for modeling regional climate. The Higher-Order Method Modeling Environment (HOMME; Taylor et al. 2008) and the Model for Prediction Across Scales (MPAS; Ringler et al. 2008; Rauscher et al. 2013) are notable examples of global models that can run using quasi-uniform and variable-resolution grids. Using unstructured grids such as the cubed sphere or Voronoi grids, these global variable-resolution models can run with high resolution in any regions without sacrificing the spatial resolution outside the region of interest as in the global stretched grid models and naturally account for scale interactions between the high- and low-resolution regions.

While the above brief review is not exhaustive, it highlights ongoing efforts at major climate modeling centers to adopt different grid refinement approaches in modeling climate at the regional scales. For these methods to produce robust simulations of regional climate, they must show a certain degree of agreement with global high-resolution simulations. At a minimum, the deviations of high-resolution climate simulations achieved through grid refinement approaches from their global high-resolution counterparts need to be characterized. Side-by-side evaluation of two models—one commonly used [Weather Research and Forecasting Model (WRF)] and one new [Model for Prediction Across Scales-Atmosphere (MPAS-A)]—is a step toward this end. In light of this background, this study aims to examine the nature of errors associated with two mesh refinement strategies: nested modeling and global variable-resolution modeling. Unlike model evaluation in which simulations of the real world are compared against observations, our approach uses an idealized model configuration of an aquaplanet (Neale and Hoskins 2000a,b) and compares simulations that achieve high resolution through grid refinement with simulations performed at high resolution globally or over a very large domain, all using the same physics parameterizations. This approach allows us to focus on errors associated with the grid refinement methods rather than on the performance of the models compared to observations, which depend on the physics parameterizations used. The aquaplanet simulation framework also simplifies the identification of errors associated with the mesh refinement strategies, which could otherwise be obscured by factors such as topography, land use, and seasonality in real-world simulations. The paper is organized as follows. The models and the design of the experiments are presented in the next section and the definition and analysis of errors in the precipitation and circulation as well as the dependence of equatorial wave propagation on the mesh-refinement strategy are presented in section 3. In the last section, the results are summarized and discussed in the context of previous studies.

2. Models and experiments

a. Models

The two models used in this study are the Community Atmosphere Model (CAM) (Neale et al. 2010), with the MPAS-A (Ringler et al. 2010, 2011; Rauscher et al. 2013; Skamarock et al. 2012) dynamical core and the Advanced Research Weather Research and Forecasting version 3.2 (WRF 3.2; Skamarock et al. 2008). MPAS-A uses Spherical Centroidal Voronoi Tessellations (SCVTs; Ringler et al. 2008) to allow local mesh refinement through specification of a scalar density function, which defines the regions of finer meshes and the extent of the grid refinement. In this study, the CAM4 physics package has also been ported to WRF 3.2 for comparison with MPAS-A that used the same physics package to isolate the effects of the dynamical framework, which includes the dynamical cores and grid refinement approaches. In CAM4, convective precipitation comes from the Zhang–McFarlane (Zhang and McFarlane 1995) cumulus parameterization scheme, which is a (convective available potential energy) CAPE-based mass flux scheme that assumes convection acts to remove the atmospheric CAPE with a prescribed relaxation time (i.e., the convective mass flux is proportional to CAPE). Large-scale precipitation is parameterized by the microphysics scheme of Rasch and Kristja‘nsson (1998), which calculates fractional cloudiness (condensate amount) from the grid-scale relative humidity. No tuning is performed to vary the model parameters for applications at different model resolutions. Although the same physics package is used in both models, subtle differences such as the order in which the various physics parameterizations are called and the state variables updated can lead to differences between the MPAS-A and WRF simulations, besides differences in the dynamical frameworks used.

b. Experiments

Three 5-yr-long aquaplanet simulations are performed with each model. Zonally uniform SST with latitudinal dependence given by if , otherwise, 0°C is prescribed. For MPAS, the global low-resolution simulation (GLR) has quasi-uniform grid spacing of approximately 120 km. The global variable-resolution simulation has a circular region of high resolution centered at the equator with a radius of 30° latitude–longitude with 30-km grid spacing. This simulation is referred to as global variable-resolution (GVR) simulation. The third simulation is also a global quasi-uniform simulation but with 30-km grid spacing [global high resolution (GHR)]. These simulations are extensively evaluated in Rauscher et al. (2013).

The corresponding WRF simulations are all performed using a tropical channel configuration (using periodic boundary conditions in the zonal direction) with a latitudinal band that ranges from 40°S to 40°N. The prescribed SST patterns are the same as above; the lateral boundary conditions are obtained from an aquaplanet simulation using a CAM4 Eulerian spectral dynamical core. In the tropical channel low-resolution run (TCLR), the spatial resolution is about 1° (~110 km) throughout the domain. In the tropical channel variable-resolution run (TCVR), a high-resolution subdomain is two-way nested in the otherwise low-resolution simulation. This configuration allows us to make a meaningful comparison with GVR to assess the effects of grid refinement approaches on the simulations in the high- and low-resolution regions. The high-resolution nested domain has grid spacing of 0.25° (about 28 km) and is a rectangular region of size 45° latitude by 90° longitude centered at the equator. Finally, the tropical channel high-resolution simulation (TCHR) has a uniform 0.25° resolution throughout the tropical channel domain.

Figure 1 summarizes the six simulations performed. Note the correspondence among the MPAS-A and WRF simulations. Since the low-resolution simulations (GLR and TCLR) have comparable spatial resolutions, the differences between them can be attributed mainly to their respective dynamical cores, although we note that implementation of the same physics packages (e.g., the order in which different physics parameterizations are called and the use of implicit versus explicit numerical schemes) in different models can also lead to some differences. That is also true when comparing the quasi-uniform high-resolution simulations (GHR and TCHR). For the variable-resolution simulations, however, the methods for introducing the high-resolution region are quite different. As discussed above, in MPAS-A the grid resolution is refined using unstructured grid from the 120-km spacing to 30-km spacing without any physical boundary, while in WRF traditional two-way nesting is applied with a physical boundary and a buffer zone of eight grid points where the simulation in the high-resolution region is nudged to the simulation in the low-resolution outer domain. In both cases, processes in the high-resolution region can affect the low-resolution region and vice versa. The variables required for the study are written out at 6-h frequency. Output from MPAS-A simulations is regridded to a latitude–longitude grid used by CAM when running with the finite-volume dynamical core using conservative remapping (Jones 1999), while the output from WRF is already on 1° × 1° grid spacing.

Fig. 1.

Schematic of the configurations of (top) three MPAS-A and (bottom) three WRF simulations with (from left to right) their grid spacings.

Fig. 1.

Schematic of the configurations of (top) three MPAS-A and (bottom) three WRF simulations with (from left to right) their grid spacings.

3. Analysis

a. Errors in the mean precipitation

For the purpose of the study using idealized experiments, error is defined as deviation of the results of the low-resolution or variable-resolution simulation from those of the global high-resolution simulations. The implicit assumption is that the global high-resolution simulation represents the “truth” because our focus is not on model skill compared to observations but rather on how well high resolution achieved through grid refinement can capture the characteristics of the global high-resolution simulations. A perfect variable-resolution simulation should, by definition, match the results of a globally uniform high-resolution simulation in the high-resolution region.

For any specific variable, the errors in the variable-resolution simulation are represented by the differences between the GHR and GVR simulations (i.e., GHR − GVR) and for WRF by the difference between TCHR and TCVR (i.e., TCHR − TCVR). Those errors may originate from the low-resolution simulations in the outer domain, and/or the limited size of the high-resolution regions. The errors can be partitioned and written as

 
formula

for MPAS-A and similarly for WRF:

 
formula

The first terms on the rhs of Eqs. (1) and (2) represent errors associated with resolution change (i.e., the resolution effect) over the whole domain. The second terms represent effects associated with the introduction of limited area high-resolution regions that would include downscale effect in the high-resolution region and an upscale effect in the low-resolution region. Since we are interested in systematic biases only, random errors are eliminated by producing an ensemble of 54 monthly means for the 4.5-yr runs and calculating the mean systematic error. A Student's t test is applied and the 4.5-yr mean difference is considered a systematic error if it is significant at the 95% confidence level. Only these significant errors are shown.

Figure 2 shows the differences in precipitation among the MPAS-A simulations. In Fig. 2a the effect of the increased resolution over the limited area region on the large-scale, convective and total precipitation is plotted [GVR − GLR in Eq. (1)]. In the region of high resolution (the circle), increased resolution increases the large-scale precipitation, but decreases the convective (nonresolved) precipitation with the net effect of increasing the total precipitation. The spatial distribution of the changes in precipitation is interesting. Increased resolution increases large-scale precipitation mainly to the immediate north and south of the equator, but the decrease in convective precipitation is mainly centered at the equator, with the net change being a more prominent double ITCZ-like feature in the total change in precipitation. Furthermore, the increased precipitation occurs primarily on the western part of the high-resolution region and even extends outside the region of highest resolution. The zonal asymmetry arises from the fact that the environmental fields that control precipitation, moisture, and temperature profiles, etc., are advected westward by the easterly winds in the tropics [see Rauscher et al. (2013) for a more extensive discussion]. Therefore, the precipitation change associated with the high-resolution simulation in a limited area is also shifted westward. In other words, a distance of almost 15° is needed before the simulation takes on high-resolution characteristics. Furthermore, there is a small but statistically significant change in precipitation over the region of low resolution far from, or mostly upstream of, the limited area high-resolution region. Outside the high-resolution region, there is a small decrease in precipitation right at the equator and small increase to the immediate south and north, suggesting a broadening of the ITCZ.

Fig. 2.

Differences in (left) large-scale, (middle) convective, and (right) total precipitation (mm day−1) from the MPAS-A simulations: (from top to bottom) GVR − GLR, GHR − GLR, and GHR − GVR. They are calculated from a sample of 5-yr monthly means and are significant at the 95% confidence level.

Fig. 2.

Differences in (left) large-scale, (middle) convective, and (right) total precipitation (mm day−1) from the MPAS-A simulations: (from top to bottom) GVR − GLR, GHR − GLR, and GHR − GVR. They are calculated from a sample of 5-yr monthly means and are significant at the 95% confidence level.

Figure 2b shows the difference between the global high- and low-resolution MPAS-A simulations (GHR − GLR). Once again, increased resolution increases the large-scale (resolved) precipitation especially slightly off the equator with no change at the equator. This pattern of change indicates a broadening of the ITCZ. This is accompanied by the decrease of convective precipitation (Fig. 2b, middle panel). These two changes more or less compensate for each other right at the equator, with the net change being mainly located off of the equator (Fig. 2b, right panel). The error in precipitation associated with variable-resolution simulation using MPAS-A (Fig. 2c) can then be explained by the responses of precipitation to the localized increased spatial resolution on the one hand and the global increase in resolution on the other as described by Eq. (1). There is little error within the high-resolution region except on its eastern end for all large-scale, convective, and total precipitation. This error on the eastern end of the high-resolution region follows from similar error associated with the zonal nonuniformity of the precipitation response within the high-resolution domain (Fig. 2a). Outside of the high-resolution region, almost all of the error in the tropics can be explained by the differences in resolution (Figs. 2b,c outside the circle), but zonal nonuniformity introduces some statistically significant signals both near the equator and over midlatitude regions as is shown in Fig. 2a (right panel).

Figure 3 shows a similar analysis of errors in precipitation for the WRF tropical channel simulations. As in the MPAS-A simulations, increased spatial resolution in the limited area increases the large-scale precipitation and decreases the convective precipitation (Fig. 3a) with a net result of increased precipitation and a broader ITCZ, which suggests that broadening of the ITCZ is a feature associated with the model microphysics scheme and is common to both dycores. However, there are some significant differences between WRF and MPAS-A. While the precipitation change with limited area regional high-resolution WRF is also zonally nonuniform, the strong increase in total precipitation is located on the eastern edge of the high-resolution domain. Further, there is a decrease in precipitation at the western end just outside the region of high resolution, in sharp contrast to what is observed in MPAS-A (Figs. 2a and 3a, right panels).

Fig. 3.

As in Fig. 2, but for the WRF simulations.

Fig. 3.

As in Fig. 2, but for the WRF simulations.

The difference between global tropical high resolution and low resolution is a zonally uniform increase in the large-scale precipitation, decrease in convective precipitation, and a small net increase in precipitation especially at the edges of the ITCZ (Fig. 3b). Moisture budget analysis of low- and high-resolution simulations in a separated study (Hagos et al. 2013, manuscript submitted to Climate Dyn.) shows that as resolution increases, the newly resolved eddies due to the increased resolution transport moisture upward and dry the boundary layer, which increase evaporation at the surface and availability of moisture. Since SSTs are prescribed, the surface fluxes are not strongly constrained by radiation. Therefore, the circulation is not weakened and the precipitation response is not moderated, as one would expect in coupled atmosphere–ocean model simulations (Held and Soden 2006). Thus, the overall error in precipitation associated with nesting in WRF can be understood in this light. Figure 3c shows that there is no significant error within the region of high resolution in the convective precipitation but there are some errors in the large-scale and total precipitation north and south of the equator.

The errors associated with nesting (i.e., the WRF simulations) tend to be concentrated at the edges. There is a particularly large error in large-scale and total precipitation just outside the western end of the high-resolution domain. This once again is related to the nesting (Fig. 3a, left and right panels). As was noted earlier, while precipitation increases with resolution, its spatial distributing is strongly affected by the nesting in WRF. Much of the increase is concentrated near the lateral edges of the domain. This error is often associated with the mismatch between large-scale forcing from the parent domain and the solution in the nested domain introducing strong convergence/divergence signals. This mismatch is believed to be fundamentally related to the fact that nesting using the common Davies approach imposes overspecification of the boundary conditions, which results in reflection of waves at the boundaries (Miguez-Macho et al. 2005; Staniforth 1997). Using idealized 1D simulations, Harris and Durran (2010) more clearly show that a mismatch in phase and phase speed of the wave modes in the high- and low-resolution regions could introduce such spurious behavior at the boundaries. Sensitivity of cloud parameterizations to resolution likely contributed to amplify the convergence–divergence signals. Spectral nudging has been shown to reduce this boundary effect (Alexandru et al. 2009), but two-way nesting as adopted in the simulations reported here appears to have little mitigating effects. The results from two-way and one-way nesting simulations (not shown) are very similar. Comparison of Figs. 3b and 3c shows that the errors outside the high-resolution region can more or less be explained by the resolution difference and two-way nesting has essentially no effect beyond the immediate neighborhood of the high-resolution region.

b. Errors in circulation

In section 3a, it was shown that a global increase in resolution enhances tropical precipitation, and variations in spatial resolution (i.e., the introduction of high resolution in a limited region) introduce some zonal nonuniformity in the precipitation, and errors in the variable-resolution simulations can be explained by the combination of the two. Errors in precipitation are manifestations of errors in condensation and associated latent heat release, which in turn would drive anomalous (erroneous) circulation. To understand the nature of the errors, let us consider the variable-resolution simulations: GVR (MPAS-A model) and TCVR (WRF Model). In the absence of zonally asymmetric forcing in aquaplanet simulations, the long-term mean circulation should be zonally uniform if there are no errors associated with the presence of the limited-area high resolution in the domain. Therefore, one can estimate the error in the circulation based on these eddy or zonally asymmetric circulations.

Figure 4 shows the anomalous (deviation from the zonal mean) circulation averaged between the surface and 700 hPa for the variable-resolution and nested simulations. Inside the regions of high resolution, the surface winds are pointing toward the anomalous precipitation (Figs. 2a and 3a), easterly in GVR and westerly in TCVR. Interestingly the presence of the high-resolution region has a remote effect throughout the domain. From linear equatorial wave theory (Gill 1980), introduction of diabatic heating associated with large-scale convection (subsidence) centered at the equator forces a pair of cyclonic (anticyclonic) circulations to the immediate northwest and southwest of the heating (Rossby waves), and divergence (convergence) to the east associated with Kelvin waves. In GVR, the diabatic heating is on the western side of the high-resolution domain and the subsidence is to the east, while in TCVR the strong convection is over the eastern end of the high-resolution domain and the subsidence is to the west, an important difference between WRF and MPAS.

Fig. 4.

(a) Anomalous (deviation from zonal mean) wind (arrows, max 2 m s−1), streamfunction (contours), and omega (shaded, Pa s−1) averaged between the surface and 700 hPa. The horizontal resolution is 30 km inside the oval and 120 km elsewhere. (b) As in (a), but for the WRF aquaplanet simulation, the rectangle is the region of high resolution and vertical velocity.

Fig. 4.

(a) Anomalous (deviation from zonal mean) wind (arrows, max 2 m s−1), streamfunction (contours), and omega (shaded, Pa s−1) averaged between the surface and 700 hPa. The horizontal resolution is 30 km inside the oval and 120 km elsewhere. (b) As in (a), but for the WRF aquaplanet simulation, the rectangle is the region of high resolution and vertical velocity.

In the above discussion, it was shown that the circulation anomalies in variable-resolution and nested models could be explained as linear responses to zonal nonuniformity in precipitation (heating) associated with the sensitivity of cloud physics to spatial resolution. Having this as a background, we return to the framework introduced at the beginning of this section to discuss the errors in circulation of variable-resolution simulations as their systematic deviations from the global high-resolution simulations. To clarify the errors in divergence and the divergent component of tropical circulation due to variable resolution and nesting, we consider the differences in near-surface velocity potential among the simulations. Figure 5 shows the differences in velocity potential among the MPAS-A (left panels) and WRF (right panels) simulations. The high resolution and associated anomalous precipitation (and heating) introduce anomalous divergent zonally oriented circulation with low-level convergence (positive velocity potential) over the region of anomalous precipitation increase (Fig. 5a). A global increase in resolution (Fig. 5b) increases convergence over the tropics and divergence over the subtropics. In other words, the Hadley circulation in both GHR and TCHR is strengthened compared to GLR and TVLR. This strengthening of Hadley circulation with resolution is also found in other aquaplanet simulations using CAM (Abiodun et al. 2008). Thus, the errors in the variable-resolution simulations (GHR − GVR and TCHR − TCVR) are the combinations of the two differences (Fig. 5c). For MPAS-A, the variable-resolution simulation overestimates the convergence at the western end of the high-resolution domain and underestimates the convergence to the east. The WRF nested simulation, on the other hand, underestimates convergence in the western edge of the domain and overestimates it on the western end. One has to keep in mind that the tropical channel WRF simulations are being forced by the CAM T85 aquaplanet simulation at the northern and southern boundaries, which could potentially constrain the response of the WRF simulations to changes in resolution. However, the experiments are designed to minimize if not eliminate this constraint by making the latitudinal extent of the tropical channel wide enough to include the subsiding branch of the Hadley cells.

Fig. 5.

The differences among the 5-yr mean velocity potentials (m2 s−1) from (left) MPAS-A and (right) WRF simulations at 970 hPa. They are calculated from the monthly means and are significant at the 95% confidence level: resolution (from top to bottom) variable − low, high − low, and high − variable.

Fig. 5.

The differences among the 5-yr mean velocity potentials (m2 s−1) from (left) MPAS-A and (right) WRF simulations at 970 hPa. They are calculated from the monthly means and are significant at the 95% confidence level: resolution (from top to bottom) variable − low, high − low, and high − variable.

The error in upper-level winds in the variable-resolution simulation can also be understood in the framework discussed above. Figure 6 shows the differences in zonal wind at 160 hPa (the level at which the zonal winds are strongest). Consistent with the fact that there is thermally direct zonally oriented circulation in the divergence field (Fig. 5a) associated with the region of high spatial resolution, there is a return anomalous flow at the upper levels (Fig. 6a). This anomalous flow is westerly in MPAS, since the anomalous heating is to the west, and easterly in WRF, since the anomalous heating is to the east. In both models, the global increase in resolution (Fig. 6b) leads to stronger easterlies in the tropics. In WRF the subtropical jet is strengthened by up to 2 m s−1, but there is slight weakening in MPAS-A. The difference between global high-resolution and the variable-resolution and nested simulations (Fig. 6c) shows that much of the error in the MPAS-A variable resolution in the tropics is related to the upper-level easterlies, which are underestimated by about 3 m s−1 east of the high-resolution domain. In WRF, the error of comparative magnitude to the immediate east of the high-resolution domain is noted.

Fig. 6.

As in Fig. 5, but for the 5-yr mean zonal wind (m s−1) from the (left) MPAS-A and (right) WRF simulations at 163 hPa. They are calculated from the monthly means and are significant at 95% confidence level.

Fig. 6.

As in Fig. 5, but for the 5-yr mean zonal wind (m s−1) from the (left) MPAS-A and (right) WRF simulations at 163 hPa. They are calculated from the monthly means and are significant at 95% confidence level.

c. Equatorial wave propagation characteristics

Equatorial waves constitute a significant component of tropical intraseasonal variability (Wheeler and Kiladis 1999) so their proper representation could be a useful metric for evaluating the fidelity variable-resolution and nested simulations. Figure 7 shows the space–time spectra of the equatorial symmetric modes from the six simulations. Both MPAS-A and WRF produce robust equatorial Kelvin and westward-propagating inertio-gravity waves (WIGs) but not long-wave Rossby signals. The WIG signals are strongest in the low-resolution simulations (GLR and TCLR) and relatively weak in the corresponding global high-resolution simulations (GHR and TCHR), but Kelvin wave signals are strong in all. In general the WRF simulations tend to have stronger high-frequency (<3-day period) signals than MPAS-A for all three experimental setups but they do not quite align along the dispersion curves, an obvious inconsistency with the observed characteristics of WIG waves. The space–time spectra of the antisymmetric modes are shown in Fig. 8. All simulations contain inertio-gravity waves, but the eastward-propagating ones are relatively weaker in WRF. In general the higher-frequency (<3-day period) signals are weaker in the high-resolution WRF simulation (TCHR). This is related to the fact that precipitation signals in WRF become particularly noisy at higher resolution. In the Wheeler–Kiladis space–time spectral analysis the relative amplitudes of these coherent high-frequency waves are measured relative to (or are divided by) the amplitudes of noise and, hence, they become smaller.

Fig. 7.

Symmetric power spectra of equatorial waves in precipitation from (top) MPAS-A and (bottom) WRF. The lines correspond to equivalent depths of 12, 25, and 50 m from bottom to top, respectively: resolution (from left to right) low, variable, and high.

Fig. 7.

Symmetric power spectra of equatorial waves in precipitation from (top) MPAS-A and (bottom) WRF. The lines correspond to equivalent depths of 12, 25, and 50 m from bottom to top, respectively: resolution (from left to right) low, variable, and high.

Fig. 8.

As in Fig. 7, but for antisymmetric power spectra.

Fig. 8.

As in Fig. 7, but for antisymmetric power spectra.

The extent to which signals are preserved in variable-resolution and nested simulations is further examined by analyzing the propagation of Kelvin waves through the domain. To isolate Kelvin waves, the equatorial symmetric part of the precipitation signal is bandpass filtered for a 3–60-day period. Figure 9 shows the propagation of the signals in the various model configurations. In both MPAS-A and WRF the signals are dominated by waves that propagate at the speed of 20–25 m s−1. The period of the dominant signals in MPAS-A is about 17 days and in WRF it is about 14 days. In general there is more high-frequency variability in WRF than in MPAS-A in all the experimental setups. In both MPAS-A and WRF variable-resolution and nested simulations (GVR and TCVR), the signals in the high-resolution region (between the dashed lines) are essentially continuations of the signals in the low-resolution regions. The variable-resolution and nested simulations preserve the propagation speed and phase of the waves well. This is in contrast with the results from the ARPEGE simulations by Lorant and Reyer (2001) that show the propagation speed of equatorial waves being strongly affected by spatial resolution variations.

Fig. 9.

Hovmöller diagram of precipitation (mm day−1) for (top) MPAS-A and (bottom) WRF simulations: resolution (from left to right) low, variable, and high.The lines mark propagation speeds of about 23 m s−1.

Fig. 9.

Hovmöller diagram of precipitation (mm day−1) for (top) MPAS-A and (bottom) WRF simulations: resolution (from left to right) low, variable, and high.The lines mark propagation speeds of about 23 m s−1.

4. Summary and discussion

Using two models with different dynamical cores and mesh refinement strategies, this study examines the nature of errors in variable-resolution and two-way nested aquaplanet simulations from the atmospheric component of Model for Prediction Across Scales-Atmosphere (MPAS-A) and the Advance Research Weather Research and Forecasting Model (WRF), respectively. WRF is run in a tropical channel mode with a latitudinal band of 40°S–40°N with lateral boundary conditions provided by a CAM4 aquaplanet simulation. Each model is run in three configurations: global low resolution (~1° grid spacing), global high resolution (~0.25° grid spacing), and variable resolution or nested (a ~0.25° grid spacing limited-area region inside a ~1° grid spacing global domain). Comparisons of monthly mean data from pairs of the 5-yr-long simulation are used to identify the nature and sources of statistically significant systematic errors in various fields.

The errors (the differences between global high-resolution and variable-resolution or nested simulations) in both models generally arise from the sensitivity of precipitation (and the associated latent heating) to resolution (Figs. 2 and 3) due to resolution-dependent model physics. This was also demonstrated in Rauscher et al. (2013), using an MPAS-A variable-resolution simulation with the Held–Suarez (1994) test configuration, in which full model physics are replaced by prescribed forcing and dissipation In this Held–Suarez test case, the zonal asymmetries were substantially smaller than in the full physics test case, implicating the resolution dependency of the physics as the cause of the errors. To the first order, the errors in circulation can be interpreted as linear responses of localized anomalous heating in the region of high resolution. The heating anomalies associated with the localized mesh refinement excite Rossby waves (Figs. 4 and 6) as well as thermally direct zonally oriented circulation features (Fig. 5). The mesh refinement strategy also appears to have an important contribution to errors. These are manifested in the form of zonal nonuniformity in precipitation in the high-resolution region. In the MPAS-A variable-resolution simulation, the increased precipitation in the high-resolution region is concentrated on the western side (Fig. 2a) because of advection by the easterly winds, hence, larger error on the eastern side. While the errors in MPAS-A are primarily due to sensitivity of the model physics parameterizations to resolution, the errors in WRF are results of both parameterization sensitivity to resolution and errors arising from the nudging approach, leading to an error pattern with increased precipitation concentrated on the eastern and western edges of the high-resolution region (Fig. 3a) almost opposite to that in MPAS-A. In both models, increased resolution enhances the large-scale precipitation north and south of the center of the ITCZ and reducing the convective precipitation at the equator resulting in a double ITCZ-like feature in the net change in total precipitation (Figs. 2b and 3b).

The propagation of equatorial waves through the variable-resolution or nested domain is examined using space–time spectra and Hovmöller diagrams. In general, the equatorial waves preserve their propagation characteristics (phase, speed, and amplitude) as they propagate through the high-resolution region of the domain.

The results summarized above, while encouraging in the sense that the variable-resolution and nested simulations preserve many critical characteristics of tropical precipitation and other fields of the high-resolution simulations, indicate that sensitivity of the magnitude of precipitation to resolution remains an important challenge because the associated localized anomalous heating and the erroneous circulation it excites have far-reaching impacts on the fidelity of the simulations. With physics parameterizations showing strong sensitivity to model resolution, the benefits of the global variable-resolution framework or two-way nesting to represent both downscaling and upscaling effects are obscured by the anomalous response to localized heating due to increased precipitation with increasing resolution. In a real-world configuration, discriminating such anomalous response from the model response to regional forcing is difficult and confounds the interpretations of regional forcing and response.

This study examines two specific models representing a global variable-resolution model and a nested model, using an identical but specific suite of physics parameterizations. Hence, our conclusions could be specific to the dynamical cores and physics parameterizations used in MPAS-A and WRF. In addition, with prescribed SSTs, the effects of resolution could be amplified as atmosphere–ocean feedbacks could potentially moderate the enhanced precipitation with increasing resolution through changes in surface energy budget and cloud–radiation feedbacks. Driven by the need for regional climate predictions, the interest in variable-resolution and nested modeling has continued to grow, so a more comprehensive evaluation of available variable-resolution and nested models, both in an idealized and real-world context, is needed to more systematically assess their relative strengths and weaknesses in comparison to the global high-resolution counterparts that they aim to replicate with reduced computational requirements.

Acknowledgments

This work is supported by the Regional and Global Climate Modeling Program of the U.S. Department of Energy Biological and Environmental Research Program. Computing resources are provided by the National Energy Research Scientific Computing Center (NERSC). Pacific Northwest National Laboratory is operated by Battelle for the U.S. Department of Energy under Contract DE-AC06-76RLO1830.

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