1. Introduction
Increasing numbers of record-breaking and devastating hydrological extremes in the past decade (Coumou and Rahmstorf 2012) has raised concerns that such extremes may have intensified in a warmer world (Allan and Soden 2008). Climate models have been used to attribute the causes of precipitation extremes (PEs) and to project the frequency and intensity of these events in the future. However, a known bias in global climate models is the prevalence of drizzle and underprediction of heavy precipitation partly as a result of the coarse spatial resolution of the models (Stephens et al. 2010). Also climate models are known to exhibit varying degrees of dependency on parameterization and model resolution (e.g., Boyle and Klein 2010; Williamson 1999). Hence, significant uncertainties exist in future PEs projected by an ensemble of climate models (Randall et al. 2007), although they generally project intensification of the hydrological cycle, with larger extremes in both floods and droughts (Held and Soden 2006).
Precipitation is difficult to characterize because of its high variability across nearly all temporal and spatial scales (Berg et al. 2013). Precipitation extremes are associated with low-frequency variability in the flow field that occasionally results in large anomalous horizontal moisture flux convergence or divergence (Held and Soden 2006). Although PEs can be defined rather unambiguously using statistical measures, the physical and dynamical mechanisms associated with PEs vary and are still not fully understood. Furthermore, global climate model (GCM) parameterizations are typically developed and tested more extensively to reproduce large-scale climatological-mean conditions. Williamson (2013) found that using typical parameter values of convective time scales (e.g., 1–2 h) assumed in shallow and convective parameterizations can cause unrealistic development of gridpoint storms producing heavy precipitation in high-resolution GCM simulations. In addition, mass-flux parameterizations (e.g., Zhang and McFarlane 1995) assume that the fractional area covered by convective clouds in a grid cell is far less than 1. The validity of this assumption becomes questionable as GCMs are applied at finer resolutions, making it necessary for parameterizations to adapt to a wider range of model resolutions (Arakawa et al. 2011), with implications to simulate the full spectrum of precipitation intensity.
With increasing high-performance computational resources, high-resolution modeling provides a promising path to improving simulations of PE. However, more research is needed to understand the sensitivity of PE to model resolutions and physics parameterizations. Williamson (1999) showed that physics parameterizations, not dynamics, are responsible for the sensitivity of model results to horizontal resolution in his GCM simulations. Li et al. (2011a,b) used an aquaplanet version of Community Atmospheric Model, version 3 (CAM3), and found that PEs are more sensitive to horizontal resolution than the mean precipitation, suggesting that the effects of horizontal resolution must be taken into account in developing robust projections of PEs. Without improvement in physics representation, increasing resolution alone may only provide limited improvement in climate models skill (Buizza 2010). Understanding the resolution dependency of PEs is an important first step toward achieving scalable and robust simulations.
This study aims to characterize the resolution dependency of extreme precipitation intensity and the variation of this dependency with dynamical cores and to estimate the relative contributions of thermodynamics and dynamics to that resolution dependency. The study is conducted using an aquaplanet framework that simplifies the analyses and interpretations in the absence of complex land–ocean contrast and land surface heterogeneity. Detailed moisture budget analyses have been performed to compare simulations produced by the Community Atmosphere Model, version 4 (CAM4) (Neale et al. 2010), with two different dynamical cores applied at a range of spatial resolution, all using the same physics parameterizations.
The rest of this paper is organized as follows: Section 2 describes the model, the aquaplanet experiments, and the simulation outputs. Section 3 discusses the analytical methods including the definition of extremes, the moisture budget equation, and the breakdowns of moisture transport to mean flow and eddy components. The characteristics of the resolution dependency in PEs and attribution of the resolution dependency are presented in section 4. The last section (section 5) summarizes the main conclusions from this study.
2. Model description and experiments
As part of the collaborative Robust Regional Modeling project (Leung et al. 2013) supported by the U.S. Department of Energy (DOE), a set of aquaplanet simulations have been conducted using the CAM4 physics package and three different dynamical cores: Model for Prediction Across Scales-Atmosphere (MPAS-A) (Rauscher et al. 2013), High Order Method Modeling Environment (HOMME) (Taylor and Fournier 2010; Evans et al. 2013), and Spectral Eulerian (EUL). Detailed model description and configuration can be found in Rauscher et al. (2013), O’Brien et al. (2013), and Leung et al. (2013). This study primarily uses simulations from the newer dynamical-core MPAS-A, with some comparison with HOMME, to provide insights on the impacts of dynamical cores on PE.
Briefly, in CAM4 the convective parameterization includes both a deep and a shallow moisture convection schemes. The shallow moist convective scheme by Hack (1994), as described in Neale et al. (2010), is used to simulate shallow and midlevel convections. The modified deep convection scheme of Zhang and McFarlane (1995) based on a plume ensemble approach in which convective-scale updrafts occur when the convective available potential energy (CAPE) exceeds a threshold value in the lower troposphere (Neale et al. 2010) is used to simulate deep convective cloud and precipitation.
Nonconvective cloud processes are parameterized by the Rasch–Kristjánsson scheme (Rasch and Kristjánsson 1998) with improved treatment of condensation and evaporation as described in Zhang et al. (2003). The Rasch–Kristjánsson scheme is a bulk microphysical scheme with both macro and micro components. It represents prognostic condensate with exchange between condensate and vapor and the associated temperature change and includes a bulk representation of conversion from condensate to precipitation (Neale et al. 2010).
The simulations used the default configuration in CAM4 consisting of 26 vertical levels in a sigma vertical coordinate with varying horizontal resolutions. Identical physics parameterizations with no adjustment for dynamical cores or spatial resolutions were used in all simulations. A set of four experiments was conducted for each dynamical core with varying resolutions (equivalent 240, 120, 60, and 30 km for MPAS-A; 220, 110, 55, 28 km for HOMME; and T42, T85, T170, and T340 for EUL). The CAM4 physics time step was set to be 10 min for all experiments.
Solar radiation is fixed to equinox solar conditions and is symmetric in the two hemispheres. Thus, seasonal and interannual variations are not represented in these aquaplanet experiments.
The analysis in this study mainly uses the archived 6-hourly data, although daily data were used to test the consistency between the scale dependency of extremes determined based on 6-hourly data and that achieved using lower temporal frequency data. The simulations with the MPAS-A dynamical core uses hexagonal grids, and they have been remapped to the corresponding finite-volume (FV) grid with equivalent resolution using conservative remapping described in Rauscher et al. (2013) to facilitate the analysis. Similar mapping to the FV grid has also been conducted for simulations with the HOMME dynamical core. Each experiment was 5-yr long and the first 6 months were considered the spinup period and excluded from the analysis. The moisture budget analysis (section 4b) is based on the 6-hourly data from the third year simulation, while the rest of the scale dependency study includes 6-hourly and daily model outputs from the full 4.5 yr of simulations. All extreme statistics provided are “mean statistics” (time and zonal averaged) for extremes, and our definition of extremes leads to 210 extreme events per latitude per year when assessed at the coarse scale (240 km) using 6-hourly data; basic statistical inferences using both the mean and variability of the extremes suggest that 1 yr of data is sufficient for statistical robustness (with ≤10% error at a 5% significance level) because of the zonal, hemispheric, and seasonal symmetry of the aquaplanet simulations.
3. Methodology
Precipitation extremes are defined, similar to O’Gorman and Schneider (2009a), as 6-hourly precipitation that exceeds the 99.9th percentile, including both wet and dry cases in a 1-yr simulation. Considering the large meridional variability in precipitation, extremes are determined by latitude. In zonally symmetric aquaplanet simulations with no seasonality, stable statistics can be obtained for extreme precipitation using all 6-hourly precipitation samples from all grid points for each latitude band in both the Northern and Southern Hemispheres.
Equation (1) is used to describe the moisture budgets for the mean conditions as well as conditions under the 99.9th percentile extremes. In the latter, the 99.9th percentile extreme events are identified based on 6-hourly precipitation data and the various terms in Eq. (1) are calculated for each event before time and space averaging. Approximately 10° latitude bands were selected to investigate the vertical characteristics of the moisture transport in more detail.
4. Results and discussion
a. Sensitivity of extremes at native grid resolution
Here analysis is performed using model outputs at the native grid resolution of the simulations (i.e., the grid resolution at which the simulations were performed). As shown in Fig. 1, the means of the precipitation extremes show large variations with the native grid resolution and temporal resolution of the data (6 hourly, 12 hourly, daily, or every 5 days) over most of the latitude ranges. The variation in extremes at the native grid resolution is much larger than that of the mean values (dashed lines in Fig. 1). Depending on the dynamical core used, the intensities of precipitation extremes vary considerably, especially over the tropics, and the extremes from the HOMME and EUL simulations show stronger variation with resolution than those from MPAS-A at their native grid (figure not shown). It is also interesting to note that for MPAS-A, increasing grid resolution to 30 km leads to double peaks at the tropics in both mean and extreme precipitation. This feature corresponding to a double intertropical convergence zone (ITCZ) has been analyzed and discussed by Landu et al. (2014) and seems to be unique to MPAS-A despite the fact that the same physics and similar grid resolutions were applied to HOMME and EUL.
Latitudinal variations of mean and extreme (≥99.9th percentile of both wet and dry conditions) precipitation with the (top) native grid resolution at different temporal data frequencies (6 hourly, 12 hourly, 24 hourly, and every 5 day) and (bottom) for the simulation at 240-km grid resolution. Because of the relatively small magnitudes, the mean values are scaled by a factor of 5 (long dashed lines).
Citation: Journal of Climate 27, 10; 10.1175/JCLI-D-13-00468.1
Motivated by the large dependency of extremes on the native grid resolution and temporal frequency of the data, we first investigate the relative contribution of different moisture budget terms to extremes using data on the native grid from MPAS-A (section 4b) to provide insights on processes that are responsible for the resolution and temporal frequency dependency. Next, we explore whether the precipitation extremes converge with increasing grid resolution and the sensitivity of the results to temporal resolution when the extreme precipitation is compared at the same grid resolution using 6-hourly and daily data (section 4c). Both simulations with the MPAS-A and HOMME dynamical cores are included in the analysis in section 4c to determine if the results are consistent among simulations with different dynamical cores. Finally, the resolution dependency of extremes is further investigated from budget analysis and the grid-scale and subgrid-scale (SGS) variability of ω.
b. Moisture budget
1) Mean versus extreme conditions
The analysis of moisture budget was carried out using 6-hourly model outputs at the native grid resolution of each simulation. Averaged over the long term, the difference between mean P and E (P − E) is roughly balanced by the divergence of the time-averaged, column-integrated moisture flux in the simulated aquaplanet atmosphere (Fig. 2), which is consistent with findings by others based on global reanalysis or global climate simulations (Trenberth and Guillemot 1995; Seager and Vecchi 2010). As shown in Fig. 2, the latitudinal variation and magnitudes of P − E are similar to those of the total advective convergence, although P − E is substantially more negative than TOTDIV over the subtropical regions. For the mean conditions, E is a significant term compared to P at all latitudes, and the tendency term is negligible (not shown).
Meridional variations of mean moisture budget terms based on simulations using the MPAS-A dynamical core with (a) 240-, (b) 120-, (c) 60-, and (d) 30-km native grid resolution. The moisture budget terms include precipitation (P, black dashed), surface evaporation (E, yellow dashed), advective moisture convergence (div, blue solid), and P − E (purple, solid).
Citation: Journal of Climate 27, 10; 10.1175/JCLI-D-13-00468.1
Meridional variations of moisture budget terms under extreme precipitation conditions based on simulations with the MPAS-A dynamical core and with (a) 240-, (b) 120-, (c) 60-, and (d) 30-km horizontal grid resolutions. Zonal, meridional, and vertical advective moisture convergence during extremes, {−u∂q/∂x}, {−υ∂q/∂y}, and {−ω∂q/∂p}, are shown in solid brown, blue, and green lines along with the corresponding total advective moisture convergence (sum, yellow solid) and extreme precipitation (P, black dashed). Note that symbols “∂” and “δ” were used interchangeably.
Citation: Journal of Climate 27, 10; 10.1175/JCLI-D-13-00468.1
2) Horizontal versus vertical advection
It is worth noting that the horizontal advective moisture convergence is very small (≤2% of total moisture convergence) compared to its vertical counterpart over the tropics, suggesting that the total advective convergence can be approximated by the vertical moisture transport {−ω∂q/∂p} over this region (Fig. 3). However, the same rule does not apply over the extratropics, where horizontal advective moisture convergence contributes up to approximately 20% of TOTDIV. Zonal advective convergence {−u∂q/∂x} is negligible at most latitude ranges except near around 30° in latitude, where negative values indicating local drying associated with the subtropical high pressure system are important, with magnitudes of roughly several percent (~7%–10%) of TOTDIV with MPAS-A.
The relative importance of moisture transport in the zonal, meridional, and vertical directions and their variations with the native grid resolution at different vertical layers are illustrated for two selected latitudinal bands (Fig. 4). A 5°S–5°N band represents the tropical region where only vertical moisture transport is important, and the 25°–35° band (including both hemispheres) represents the extratropical regions where zonal, meridional, and vertical moisture advective transport are all nonnegligible. Consistent with the previous results, the moisture transport over both latitude bands is dominated by the vertical moisture transport (Fig. 4), which shows a strong sensitivity to the model’s native grid resolution. The vertical moisture transport peaks at the midatmosphere (~600 and ~700 hPa for the tropical and subtropical bands, respectively), where its sensitivity to the native grid resolution is also the largest. Zonal and meridional transport is negligible over the tropics, but over the extratropical band, zonal and meridional transport also plays a role especially in the lower atmosphere. Over this region, zonal moisture transport −u∂q/∂x contributes to the drying of the atmosphere below approximately 650 hPa, and this term increases slightly in magnitude with increasing native grid resolution below approximately 800 hPa. The meridional moisture transport over the extratropical band has magnitudes comparable to the vertical moisture transport near the surface layer (p > 900 hPa), but decreases with height and becomes fairly small above 400 hPa. The meridional transport −υ∂q/∂y over this region shows a slight converging tendency with similar values at high resolution. Over both tropical and extratropical bands, the variation of TOTDIV during extremes with the native grid resolution is dominated by the corresponding variation in vertical moisture transport that maximizes in the midtroposphere, where the dependency on the native grid resolution is also the greatest.
Vertical profiles of zonal (−u∂q/∂x, brown), meridional (−υ∂q/∂y, blue), and vertical (−ω∂q/∂p, green) advective moisture convergence for simulations at their native grid resolutions of 30- (dashed–dotted–dotted), 60- (dotted), 120- (dashed), and 240-km (solid) with the MPAS-A dynamical core for latitude bands of (a) 5°S–5°N and (b) 25°–35° in both hemispheres. Note that symbols “∂” and “δ” were used interchangeably.
Citation: Journal of Climate 27, 10; 10.1175/JCLI-D-13-00468.1
3) Mean fields versus transient eddies
The vertical advective convergence is further partitioned into mean fields and transient eddy components according to Eq. (2) (Fig. 5 for MPAS-A) to estimate the relative contributions of mean circulation and eddies to extremes. Over both the tropics and extratropics, the eddy transport of mean moisture {−ω′∂[q]/∂p} is the dominant term, followed by eddy transport of eddy moisture {−ω′∂q′/∂p}. While these two terms are comparable in magnitude over the extratropics (e.g., 76.4 versus 53.5 mm day−1 over 30°–35°N at 30 km with MPAS-A), the former is several times higher (e.g., 377.8 versus 76.4 mm day−1 over 5°S–5°N at 30-km resolution with MPAS-A) than the latter over the tropics. The mean flow term {−[ω]∂[q]/∂p} is not significant (<0.8 mm day−1 with MPAS-A) at all latitudes except over a narrow band centered at the equator where it shows converging tendency with increasing native grid resolution in MPAS-A (11.5, 13.5, 14.4, and 14.5 mm day−1 for 240, 120, 60, and 30 km). The third term of Eq. (2) {−[ω]∂q′/∂p} is negligible (<0.05 mm day−1 over the tropics and extratropics). Thus, the large variation of the vertical advective moisture transport at the native grid resolution is mainly coming from that of the two eddy terms {−ω′∂[q]/∂p} and {−ω′∂q′/∂p}.
The breakdown of vertical advective moisture convergence during extremes into corresponding mean flow, {−[ω]∂[q]/∂p} (brown solid), and two eddies-related terms, {−ω′∂q′/∂p} (yellow dotted) and {−ω′∂[q]/∂p} (green dashed), for the MPAS-A simulations at four native grid resolutions of (a) 240, (b) 120, (c) 60, and (d) 30 km. The total vertical advective moisture convergence (sum) and precipitation (P) during extremes are also shown as black dashed and dotted lines, respectively. Note that symbols “∂” and “δ” were used interchangeably.
Citation: Journal of Climate 27, 10; 10.1175/JCLI-D-13-00468.1
Similar breakdowns of zonal and meridional advective convergence found that zonal-mean flow transport of eddy moisture {−[u]∂q′/∂x} and meridional eddy transport of eddy moisture {−υ′∂q′/∂y} (Fig. 6) are only significant over the extratropical subtropical band during extremes where {−[u]∂q′/∂x} slightly dries the storm at most vertical levels, while {−υ′∂q′/∂y} along with vertical moisture transport supply moisture for the extreme precipitation over this region. In the lower atmosphere (p > ~850 hPa), the vertical eddy transport of eddy moisture −ω′∂q′/∂p contributes negatively to P during extremes over both the tropics and extratropics. Although both instantaneous q and large-scale [q] decreases with height, q′ peaks at around 850–875 hPa vertically (figure not shown). This is likely to result from low-level convergence, especially that at the zonal direction, which brings drier and colder air from the outer region to the convective center. As a result of the reverse vertical gradients of q′ and the strong upward eddy motion, −ω′∂q′/∂p dries the lower level and contributes negatively to precipitation intensity during extremes. Over the tropics, the source of moisture, its associated energy, and the resolution dependency of the moisture transport at the native grid resolution are dominated by eddy transport of mean moisture −ω′∂[q]/∂p. However, over the extratropics, this is true only for the lower altitudes (p > ~700 hPa) while at higher altitudes (p < ~700 hPa), the resolution dependency in the moisture transport is dominated by the eddy transport of eddy moisture −ω′∂q′/∂p. At the midlayer (~700 < p < ~800 hPa), both eddy terms are comparable in terms of their contributions to the total moisture convergence and its resolution dependency.
Vertical profiles of mean flow and eddy moisture transport for simulations at the native grid resolutions of 30 (dashed–dotted), 60 (dotted), 120 (dashed), and 240 km (solid) with the MPAS-A dynamical core for the latitude bands of (a) 5°S–5°N and (b) 25°–35° (including both hemispheres). The mean flow and eddies terms are too small and are omitted. Note that symbol “∂” is equivalent to “δ” in Eq. (2).
Citation: Journal of Climate 27, 10; 10.1175/JCLI-D-13-00468.1
In profiles of moisture and ω (not shown), it is indicated that the resolution dependency of ω assessed at the native grid resolution is large, which is passed on to the vertical moisture transport terms. The vertical moisture structures in mean and eddy quantities act as an averaging kernel, which determines the relative contribution from different levels to the overall scale dependency and magnitude of the column-integrated moisture transport assessed at the native grid resolution. Over the tropics, the mean atmosphere is already very humid (~13 g kg−1 near surface), and [q] decreases very sharply with the increasing altitude. As a result, the vertical gradients of [q] are much larger than that of q′, which in addition to the more significant drying at the lower atmosphere associated with the reverse vertical moisture gradients results in larger magnitude and larger resolution dependency of {−ω′∂[q]/∂p} than {−ω′∂q′/∂p} over the tropics. Over the extratropics, however, the mean atmosphere above approximately 700 hPa is much drier and has a small vertical gradient compared to that under extreme conditions, which explains the dominance of {−ω′∂q′/∂p} over {−ω′∂[q]/∂p} in magnitudes and dependency on the native grid resolution for the upper atmosphere over this region.
4) Dynamics versus thermodynamics
Estimated differences in vertical advective convergence [Δ(ωδq/δp), green] between simulations at fine resolutions (30, 60, and 120 km) and that at the coarse resolution (240 km) during extremes and the contributions to these differences by changes in dynamics [Δ(ω)δq/δp, blue], thermodynamics [ωΔ(δq/δp), yellow], and their covariance changes [Δ(ω)Δ(δq/δp), black] relative to the coarse resolution (240 km). The estimates in this figure are based on simulations with the MPAS-A dynamical core and at their native grid resolution.
Citation: Journal of Climate 27, 10; 10.1175/JCLI-D-13-00468.1
c. Scale dependency at the same grid scale
Because coarse-resolution simulations cannot produce the fine-scale features resolvable by the high-resolution simulations, a more useful analysis of resolution dependency is to compare simulations aggregated to the same spatial resolution. For such an analysis, the resolution dependency is represented by the difference Δ between the fine- and coarse-resolution simulations after the fine-resolution simulations have been aggregated or upscaled to the coarse-resolution grid using area-weighted averaging. We define convergence as the time-averaged zonal mean of extremes in simulations performed at different grid resolutions but aggregated to the same coarse resolution are not statistically different (at a 5% significance level) from each other. That is, simulations performed at a range of grid resolutions do not exhibit a resolution dependency when they are aggregated to the same grid resolution for comparison. Figure 8 shows the zonal-averaged mean and extreme precipitation for simulations performed at 30-, 60-, 120-, and 240-km grid resolution, all compared at the 240-km grid resolution for MPAS-A, and similarly for HOMME. Interestingly, the double ITCZ feature simulated at 30-km resolution simulation with MPAS-A disappears or becomes inconspicuous after upscaling to the coarse grid, which indicates the association of this feature with small-scale variability. Neither mean nor extreme precipitation shows convergence over the tropics, and the differences between high- and low-resolution simulations do not vary monotonically with grid resolution. This is seen more clearly for extremes in Fig. 9 that show the difference Δ between higher-resolution simulations aggregated to 240-km grid resolution and the coarse-resolution simulation performed at 240-km grid resolution. There is no convergence of extremes over the tropics (i.e., Δ is statistically different from zero) in MPAS-A at 6-hourly and daily time scales. The same is true when assessed at 120- or 60-km grid scales for the MPAS-A simulations using 6-hourly, 12-hourly, or daily data (not shown). Similarly, simulations with HOMME do not converge at 6-hourly or daily time scales over the tropics.
Variations of mean and extreme precipitation with grid resolution assessed at the same grid scale for simulations with the (top) MPAS-A and (bottom) HOMME dynamical cores. The simulations conducted at fine resolutions have been aggregated (area-weighted averaged) to the coarse-resolution grids (240 km for MPAS-A and 220 km for HOMME). The mean values are scaled by a factor of 5 (long dashed lines) because of their relatively small magnitudes.
Citation: Journal of Climate 27, 10; 10.1175/JCLI-D-13-00468.1
Differences of extreme precipitation between fine (120, 60, and 30 km for MPAS-A and 110, 55, and 28 km for HOMME) and coarse resolutions (240 km for MPAS-A and 220 km for HOMME) when assessed at the same grid using both (a),(c) 6-hourly and (b),(d) daily data. The simulations conducted at fine resolutions have been aggregated (area-weighted averaged) to the coarse-resolution grids (240 km for MPAS-A and 220 km for HOMME) before calculating the differences. The gray area indicates that the 95% confidence interval within which the two fine-resolution simulations are not statistically different.
Citation: Journal of Climate 27, 10; 10.1175/JCLI-D-13-00468.1
Over the extratropics, for both dynamical cores, Fig. 9 shows that the simulations do not converge when compared at the coarse grid scale except for a small latitude range (~20°–25°, including both hemispheres) for MPAS-A. The magnitudes of extremes from the coarse-resolution simulations (blue lines in Fig. 8) are much lower than that from the finer grid resolutions, and there is a poleward shift of the extratropical peak (~30° in latitude) from coarse to fine resolutions. The poleward shift is even more apparent when the simulations are compared at their native grid resolution (Fig. 1). The scale dependency is reduced when coarser temporal resolution data are used over the extratropical regions. As shown in Fig. 9, at the daily time scale, the differences between high- and low-resolution simulations become negligible so the four simulations performed at grid resolutions ranging from 30 to 240 km essentially converged at a wide range of latitudes (e.g., 50°–65° for MPAS-A). When assessed at the 120-km scale using 6-hourly data, simulations at 60- and 30-km resolution with the MPAS-A converge over 20°–50° in latitude (figure not shown). When assessed at the 120-km scale using daily data, simulations with MPAS-A converge in the latitude range of 15°–60° (figure not shown). The scale dependency of simulations with HOMME over the extratropics region is similar but generally larger than that with MPAS-A (Fig. 9). There is no converging tendency over the high latitudes (>70°) for simulations with both dynamical cores. We note, however, that near the poles, sampling becomes an issue as the number of grid cells becomes much smaller.
The dynamical and thermodynamical contributions to the scale dependency of extremes compared at the same grid scale are shown in Fig. 10 for the tropical and extratropical bands. The contributions from thermodynamic changes are generally consistent between MPAS-A and HOMME. When assessed at the same coarse grid scale, thermodynamic (moisture) changes become significant in offsetting the dynamic effect (ω), especially over the extratropics, although contributions from dynamic changes to the scale dependency is still larger and explain most of the scale dependency of the vertical advective moisture convergence. Contributions of thermodynamic changes are negative within most vertical layers over both the tropics and extratropics for both dynamical cores, thus reducing the overall scale dependency. The offsetting thermodynamic effects are associated with the decrease in specific humidity with resolution for both mean and extreme conditions with either dynamical core. The contributions of dynamic changes to scale dependency are positive except over the tropics for MPAS-A where their contributions are negative.
Contributions of dynamics [Δ(ω)δq/δp, blue], thermodynamics [ωΔ(δq/δp), yellow], and their covariance changes [Δ(ω)Δ(δq/δp), black] to the scale dependency of vertical advective convergence [Δ(ωδq/δp), green] for simulations with the (a),(b) MPAS-A and (c),(d) HOMME dynamical cores. The changes are estimated as differences relative to the coarse resolution (240 km for MPAS-A and 220 km for HOMME) at the same grid scale.
Citation: Journal of Climate 27, 10; 10.1175/JCLI-D-13-00468.1
Over the tropics, with the MPAS-A dynamical core, both dynamical changes and thermodynamical changes become more negative with increasing resolution (Fig. 10a), so the extremes do not converge. Although thermodynamical changes offset some of the scale dependency caused by the dynamics with HOMME over the tropics, the scale dependency from dynamics contributions is several times larger in magnitude than that over the extratropics (note the different scales used in the x axis for Figs. 10c,d). The scale dependency remains too large for the simulations to converge even when assessed using daily data.
At the upper atmosphere (<~300 hPa) in the 58-km simulation with HOMME, the resolution dependency is mainly explained by changes in thermodynamics over both latitudinal bands, which is an exception. This is likely as a result of the higher convective cloud tops simulated at 58-km resolution with HOMME. A slightly more humid atmosphere (especially above ~700 hPa) is seen in the 58-km simulation with HOMME under both mean and extreme conditions, and the more humid atmosphere allows storms to reach higher tops. The differences in thermodynamics in the HOMME simulations at the upper atmosphere are likely influenced by nonlinear feedbacks from large changes in dynamics, which require further investigation.
The dominant contributions of dynamics changes to scale dependency of the vertical moisture transport during extremes warrant further examination of the sensitivity of ω with resolution. As indicated by the vertical velocity spectra in Lean and Clark (2003), the vertical velocity in a convective system consists of variability at scales much smaller than the finest grid spacing used in our experiments. When upscaled to a coarse grid scale through averaging, signals/variances at scales smaller than the analysis scale are reduced at coarser resolution, so the mismatch of process and analysis scales often leads to difficulty in producing reliable statistics from aggregating areal data (McComiskey and Feingold 2012). While data aggregation does not alter the mean values, it does impact extreme intensities since extremes represent events with high temporal and spatial variability.
The probability density functions (PDFs) of the simulated ω at their native grid (e.g., the red dashed, green dotted, and blue solid curves in Fig. 11 corresponding to PDFs of ω from simulations performed at 60/58, 120/110, and 240/220 km, respectively) become increasingly broader accompanied by more extreme tail values with the increase in native grid resolution. The differences of PDFs at the same coarse grid scale [e.g., 
Resolution dependency of PDFs of −1ω (at 600 hPa) for the (a),(b) 5°S–5°N and (c),(d) 25°–35° (including both hemispheres) latitude bands. Colors indicate the native grid resolutions in which the simulations were conducted. In the PDF, the different line styles indicate the coarse grid scale to which the fine-resolution simulations have been aggregated, and the corresponding vertical line indicates the 99.9th percentile of the negative ω.
Citation: Journal of Climate 27, 10; 10.1175/JCLI-D-13-00468.1
Following the above analysis, the sensitivity of extreme vertical velocity to spatial grid spacing is illustrated quantitatively in Fig. 12, along with those of the mean vertical velocity. With both MPAS-A and HOMME, the mean negative ω at 600 hPa is positive (upward) and in general increases with increasing resolution over both tropical and extratropical bands and show monotonic converging tendency over extratropical regions.
(a),(d) The mean negative ω and (b),(c),(e),(f) the same grid-scale differences (ΔGS) in the 99.9th percentile of negative ω on 600 hPa for (top) 5°S–5°N and (bottom) 25°–35° (including both hemispheres) latitude bands based on simulations with the MPAS-A or HOMME dynamical cores. The x axis indicates the native grid resolution the simulations were conducted in, and the solid lines, dashed lines, and filled circles indicate the grid scales of 240, 120, and 60 km for MPAS and 220, 110, and 55 km for HOMME, respectively. The fine-resolution simulations were aggregated to for the grid-scale comparison.
Citation: Journal of Climate 27, 10; 10.1175/JCLI-D-13-00468.1
The sensitivity of extreme vertical velocity to resolution is different from that of the means. The 99.9th percentiles of the negative 
The intensities of precipitation extremes and the corresponding high percentile vertical motions are much higher in HOMME than MPAS-A over the tropics. This could be explained partly by the 20% higher effective resolution with HOMME compared to MPAS-A at similar grid resolution (figure not shown). Comparison of the kinetic energy spectra from MPAS-A and HOMME reveals that MPAS-A is slightly more dissipative than HOMME (figure not shown); however, the differences are relatively small and unlikely to be the main reason for the large differences from MPAS-A regarding extreme precipitation over the tropics. A 1-yr HOMME test run replacing the vertical discretization approach from Simmons and Burridge (1981) used in the HOMME simulations analyzed in this study by the vertical Lagrangian method reduces the mean precipitation simulated by 15% near the equator, which brings the HOMME simulations closer to MPAS-A in terms of the mean precipitation values over the tropics. However, changing the vertical discretization approach in HOMME appears to have little impacts on the extreme precipitation. Further investigation is required to identify the main reason leading to the large differences between HOMME and MPAS-A simulations when the same CAM4 physics package is used.
5. Summary and conclusions
In this study, we examine the resolution dependency of precipitation extremes in climate models. This has implications for projecting changes in climate variability and extremes in the future. A set of aquaplanet simulations produced by a global model using the same physics parameterizations but different dynamical cores and horizontal grid resolutions were used in this investigation. Strong increases of precipitation extremes with native grid resolutions are seen over both the tropics and extratropics. The magnitude of this dependency also varies with dynamical cores, especially over the tropics. Moisture budget estimates based on the aquaplanet simulations with MPAS-A suggest that during precipitation extremes, surface precipitation is approximately balanced by the advective moisture convergence with evaporation contributing an insignificant amount, although evaporation plays a much larger role in providing moisture for the mean precipitation. This is particularly true over the tropics, where the vertical advection of moisture explains nearly all of the surface precipitation during precipitation extremes. Over the extratropics, where the contribution of vertical moisture transport still dominates the total moisture transport, meridional advection also contributes.
The variation of moisture transport with the native grid resolution is mainly as a result of the eddy transport of mean moisture {−ω′∂[q]/∂p} and the eddy transport of eddy moisture {−ω′∂q′/∂p}. At most vertical levels over the tropics and in the lower atmosphere over the extratropics, the interaction between eddies and the mean moisture field {−ω′∂[q]/∂p} dominates the contribution to precipitation extremes. Over the extratropics, the source of moisture and its associated energy are dominated by eddy transport {−ω′∂q′/∂p} at the mid- and upper troposphere. With both the MPAS-A and HOMME dynamical cores, the resolution dependency of the vertical advective moisture convergence during extremes is mainly explained by dynamical changes (related to ω). Although the vertical gradients of moisture act like averaging kernels that determine the relative contributions of the changes in ω at different vertical levels to the overall scale dependency. The scale dependency of extremes is also assessed by aggregating (using area-weighted averages) the fine-resolution simulations to the coarse-resolution grids for comparison. The extreme precipitation does not converge with resolution over the tropics for simulations with either MPAS-A or HOMME when all simulations are compared at 240/220 km (and also at finer grid scales) with either 6-hourly or daily data. With either MPAS-A or HOMME, over the extratropics, extremes do not converge at the coarse grid scale (240 km for MPAS-A and 220 km for HOMME) at most latitudes. However, this scale dependency is reduced when coarser temporal resolution data are used, and convergence in extremes is found with daily data over a wide range of latitudes in the extratropics. In addition, there is a poleward shift in the extratropical peak of the extreme precipitation (~30° in latitude) from coarse to fine resolutions, which is very clear when comparing simulations at their native grid resolution and still apparent even when comparing simulations that are aggregated to the coarse scale.
When assessed at the same grid scale through aggregation of the finer-resolution simulations, thermodynamic (moisture) changes become significant in offsetting the effect of dynamics (ω), especially over the extratropics, although dynamics still show a more dominant impact on the resolution dependency than thermodynamics over most vertical layers, especially in the midtroposphere where the resolution dependency in vertical moisture transport is the largest.
This study shows that extreme precipitation in aquaplanet simulations using the Community Atmosphere Model (CAM) demonstrates spatial resolution and dynamical-core dependency, especially over the tropics, despite the fact that the same physics parameterizations were used. Simulations with the HOMME dynamical core shows higher variability in the vertical motion, leading to higher extreme precipitation intensities and a resolution dependency beyond what can be explained by a 20% higher effective resolution in HOMME compared to MPAS-A, which requires further investigation. Differences in simulations compared at the same grid scale suggest that the effects of subgrid variability in ω and vertical moisture transport during extreme conditions are not adequately parameterized at coarse resolutions in both MPAS-A and HOMME and more so for the latter.
Li et al. (2011b) have also identified ω as the source of resolution dependency of extreme precipitation in aquaplanet simulations using simple correlation coefficients to attribute the likely causes. This study quantifies the relationship between ω and extreme precipitation using a detailed moisture budget equation, with an added focus on comparing how the relationship varies with dynamical cores. Sugiyama et al. (2010) showed that changes of PE under global warming are strongly linked to the magnitude and profile of vertical velocity in the tropics. GCM projections of future PEs have been found to be very sensitive to model resolution and parameterizations (O’Gorman and Schneider 2009b). Hence, the resolution and dynamical-core dependency of extreme precipitation has important implications to the prediction of future changes in extreme precipitation.
Williamson (2008) discussed the behavior of extreme precipitation in the equatorial region (10°S–10°N) in the form of the probability density function using simulations with the CAM finite-volume dynamical core. Our analysis extends his study by including results from different dynamical cores. In light of the sensitivity of extreme precipitation and vertical velocity to dynamical cores, in addition to model resolution, future studies should further investigate how dynamical cores interact with model resolution and physics parameterization to influence extreme precipitation. Future development in convective parameterizations needs to address not only spatial-resolution dependency but also dynamical-core dependency. Convective parameterizations that incorporate probability density functions of ω might better capture the variability of vertical motion during extremes and improve consistency of extreme precipitation intensity simulated with different dynamical cores at a different spatial resolution. The aquaplanet framework and analysis described in this study provide an important metric for assessing the sensitivity of cloud parameterizations to spatial resolution as well as dynamical cores under extreme conditions.
Acknowledgments
We thank Samson Hagos and Kiranmayi Landu for the helpful discussion and the internal review of this manuscript. This research was supported by the Office of Science of the U.S. Department of Energy as part of the Regional and Global Climate Modeling program. The Pacific Northwest National Laboratory is operated for DOE by Battelle Memorial Institute under Contract DE-AC05-76RL01830.
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