Geophysical Research Letters RESEARCH LETTER 10.1002/2015GL066713 Key Points: • The manifestation of convection in RCE strongly depends on horizontal grid spacing • Reduced planet setups mimic the RCE behavior of full planet simulations with equivalent grid spacing • RCE provides a framework to directly compare high-resolution AGCMs to CRMs
Supporting Information: • Supporting Information S1
Correspondence to: K. A. Reed,
[email protected]
Citation: Reed, K. A., and B. Medeiros (2016), A reduced complexity framework to bridge the gap between AGCMs and cloud-resolving models, Geophys. Res. Lett., 43, 860–866, doi:10.1002/2015GL066713.
Received 22 OCT 2015 Accepted 13 DEC 2015 Accepted article online 16 DEC 2015 Published online 16 JAN 2016
A reduced complexity framework to bridge the gap between AGCMs and cloud-resolving models Kevin A. Reed1 and Brian Medeiros2 1 School of Marine and Atmospheric Sciences, State University of New York at Stony Brook, Stony Brook, New York, USA, 2 Climate and Global Dynamics Laboratory, National Center for Atmospheric Research, Boulder, Colorado, USA
Abstract
The role of convective parameterizations at high horizontal resolution and their impacts on clouds, circulation, and precipitation processes represent large uncertainties in atmospheric general circulation models (AGCMs). As the statistical equilibrium in which radiative cooling is balanced by convective heating, radiative-convective equilibrium (RCE) offers a simplified framework to investigate such uncertainties. The Community Atmosphere Model 5 is configured in a RCE setup that consists of an ocean-covered planet with diurnally varying, spatially uniform insolation with no rotation effects. A series of simulations are performed in which the planetary radius is incrementally reduced. Because of the homogeneity of the setup, the effect is to reduce grid spacing, mimicking increased resolution without increasing the number of grid points. The results suggest that the reduced planet approach is able to reproduce the behavior of convection from full high-resolution simulations. At grid spacing less than 20 km, convective motions are predominantly produced by resolved scales.
1. Introduction A growing literature has demonstrated the usefulness of radiative-convective equilibrium (RCE) for furthering our understanding of the atmosphere, as well as aiding in model development. Initially studied using single column models [e.g., Manabe and Strickler, 1964], recent decades have seen RCE investigated in a variety of modeling frameworks, from more complex single column models to three-dimensional cloud-resolving models (CRMs). Recent studies with CRMs have focused on a range of phenomena, including understanding convective aggregation [e.g., Bretherton et al., 2005; Muller and Held, 2012; Wing and Emanuel, 2014; Wing and Cronin, 2015] and tropical cyclones [e.g., Nolan, 2007; Nolan and Rappin, 2008; Chavas and Emanuel, 2014]. In addition to studies at cloud-resolving scales, RCE has been investigated in atmospheric general circulation models (AGCMs) at much coarser horizontal resolutions in which convection needs to be parameterized. Work by Held et al. [2007] with the Geophysical Fluid Dynamics Laboratory (GFDL) Atmospheric Model (AM) 2 studied RCE in a large-domain model with periodic boundary conditions at grid spacings greater than 100 km to understand the impact of prescribed sea surface temperatures (SSTs) and horizontal resolution on convection in the absence of rotation. Held and Zhao [2008] and Zhou et al. [2014] took the framework a step further by adding uniform rotation to study the characteristics of the constituent tropical cyclones in the same model. Shi and Bretherton [2014] studied RCE in the context of realistic rotation and prescribed globally constant SSTs in GFDL AM. Furthermore, Popke et al. [2013] and Becker and Stevens [2014] utilized ECHAM6 developed at Max Planck Institute for Meteorology in a global RCE framework to explore global climate sensitivity. Finally, Reed et al. [2015] and Reed and Chavas [2015] used a similar nonrotating and uniformly rotating global RCE setup in the Community Atmosphere Model 5 (CAM5) to evaluate cloud and circulation sensitivities at next-generation horizontal resolutions (i.e., less than 30 km grid spacing), while Arnold and Randall [2015] used a superparameterized version of CAM to explore global-scale aggregation in the RCE context.
©2015. American Geophysical Union. All Rights Reserved.
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Overall, RCE has demonstrated to be a useful framework at various length scales and in a range of model setups. As the horizontal resolution of AGCMs continues to approach cloud-system-resolving scales, it is easy to envision an eventual overlap in the scales associated with CRMs and AGCMs. This study offers a first look at utilizing a comprehensive AGCM, in this case CAM5, at cloud-system-resolving scales (i.e., grid spacings less than 10 km) in the RCE framework. To achieve these resolutions at reduced computational costs, a configuration is introduced in which the number of grid points remains fixed while the radius of the planet is decreased, REDUCED COMPLEXITY MODELING
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Table 1. Grid Spacing, Horizontal Resolution, Time Step, and Fourth-Order Diffusion Coefficient Details for the Reduced Planet Simulations Approximate Grid Spacing (km)
Equivalent Resolution
Dynamics Time Step (s)
Diffusion Coefficient (m4 s−1 )
1 times
111
ne30
900
1.0E+15
2 times
56
ne60
450
1.0E+14
4 times
28
ne120
225
1.0E+13
8 times
14
ne240
112.5
1.0E+12
16 times
7
ne480
56.25
1.0E+11
Reduction Factor
effectively decreasing the domain size (surface area) and the grid spacing of the AGCM. This configuration preserves the characteristics of a global model, in particular the spherical geometry, with no changes in the underlying equations of motion or parameterized physics. The main goal of this paper is to demonstrate that this reduced planet RCE framework behaves properly, offering the potential for direct comparison of CAM5 to state-of-the-art CRMs. It is worth noting that complimentary attempts are being made to run CRMs with near-global-scale domains in typical AGCM setups such as aquaplanets [Bretherton and Khairoutdinov, 2015]. This paper is organized in the following manner. Section 2 provides a brief description of CAM5 and the model configuration. Section 3 presents an initial analysis of the framework at a variety of horizontal grid spacings. The paper concludes with a discussion of the results in section 4.
2. Experimental Setup The Community Atmosphere Model 5 (CAM5) released as part of the Community Earth System Model version 1.2.1 is used for this study (downloadable at http://www.cesm.ucar.edu/models/cesm1.2/). CAM5 is configured with the spectral element dynamical core on a cubed-sphere grid [Taylor and Fournier, 2010; Dennis et al., 2012], and a detailed description of the model is provided in Neale et al. [2012]. The model physics package includes the deep convection parameterization described in Zhang and McFarlane [1995] and the shallow convection parameterization documented in Park and Bretherton [2009]. All simulations presented in this study utilize the default physics tuning parameters from the ne30 resolution, where ne represents the number of elements along the cube edge. This results in exactly 48,602 grid points, and the grid spacing of about 111 km represents a typical resolution utilized for climate simulation with CAM5 for the Coupled Model Intercomparison Project phase 5 [Taylor et al., 2012]. The simulations are set up in a similar manner to the RCE framework presented in Reed et al. [2015] (hereafter referred to as R15), in which CAM5 is utilized in an aquaplanet configuration with three additional modifications: (1) a global constant prescribed SST of 29∘ C; (2) spatially uniform, but diurnally varying, insolation which, when averaged over the diurnal cycle, approximates the observed global annual mean insolation; and (3) no rotation effects (i.e., no planetary rotation). Other design choices include the removal of direct and indirect effects of aerosols, a horizontally uniform vertical profile of ozone, and a fixed surface albedo. For further specifics of the experimental design refer to R15. This study introduces one additional modification: a reduction in the planetary radius. By reducing the planet’s radius, the impact of horizontal resolution in the RCE framework can be explored at reduced computational cost. In particular, a series of five 2-year-long simulations in which the radius of the planet is reduced by a factor of 2 are performed ranging from the control configuration grid spacing of 111 km to a grid spacing of 7 km. It should be noted that the spectral element package is a hydrostatic dynamical core, and while a nonhydrostatic version of the core is under development, it is not feasible to push further into the nonhydrostatic regime at this time. In addition to the reduction in radius, the dynamics time step and the fourth-order hyper-diffusion coefficient is decreased accordingly (see Table 1). In all simulations the time step at which the physics forcing is applied remains constant at 900 s to avoid known sensitivity of the parameterizations to this time step [Reed et al., 2012; Williamson, 2013]. The approach of reducing the size of the planet to investigate high horizontal REED AND MEDEIROS
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Figure 1. Monthly averaged (left column) cloud fraction in contours and lowermost model level winds as vectors and (right column) total precipitation for the RCE simulations for a randomly selected month. Results are shown for each grid spacing (see labels).
resolution has been suggested in the past to explore large-scale circulation at cloud-resolving scales [Kuang et al., 2005] and for model evaluation with idealized nonhydrostatic test cases [Klemp et al., 2015]. This study further demonstrates the usefulness of this approach in nonrotating RCE.
3. Results Figure 1 provides a qualitative view of the resulting RCE state for all five simulations. In particular, the figure shows the monthly averaged (Figure 1, left column) cloud cover and near-surface wind vectors and (Figure 1, right column) total precipitation for an arbitrary month. In all cases, convection has organized into coherent convective clusters as evidenced by convergence toward regions of high precipitation rates and cloud fraction. However, the structure of the clusters varies depending on grid spacing. In the default configuration, the RCE state manifests as a single cluster, whereas at 55 km and 28 km the convection organizes in to ribbon-like structures. At the smallest grid spacings the convective regions are again organized REED AND MEDEIROS
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into a single circular structure that is very well defined with sharp boundaries, which is consistent with CRM studies [e.g., Bretherton et al., 2005; Wing and Emanuel, 2014]. The figure shows the full domain which contains the same number of grid points for each simulation, but it is worth noting that the whole 7 km domain is much smaller in area than the large convective cluster shown in the 111 km domain. The dependence of convective organization on grid spacing in CAM5 has been discussed in detail in R15, and Figure 1 offers a direct comparison to the results of Figure 1 in that study. The default configuration with 111 km grid spacing is directly comparable to the ne30 simulation in R15; the only difference being the length of the physics time step (900 s in this work and 1800 s in R15). The Figure 2. Probability density functions of the 6-hourly averaged total precipitation (solid lines) and convective shorter physics time step used in this study results precipitation (dashed lines) for the second year of each in increased intensity of precipitation compared simulation. Data from the full-sized planet high-resolution to the previous published result (this is also evi(ne120) simulation from Reed et al. [2015] are provided as dent from the results shown in Figure 2 below). the gray lines for comparison. The data are binned in This result is consistent with the work of Williamson 3 mm/d bins. [2013] which demonstrated that short physics time steps allow less time for instabilities and supersaturation to be removed by the model’s convection parameterizations, due to their relatively long convective time scales, forcing the prognostic (i.e., resolved-scale) precipitation scheme to remove the supersaturation. As a reminder, the physics time step is 900 s for all simulations in the present study. In addition, the ne120 simulation in R15 (with no reduction in planetary radius) provides the equivalent grid spacing of the 28 km simulation (with a reduction in planetary radius) in this study. When comparing the two 28 km simulations, the difference is that the reduced planet simulation presented here has 16 times fewer grid points, representing the decrease in the planet’s surface area. The convective structures shown in Figure 1 are very similar to those in R15, but there is less area in which the structures can form, and consequently, there is only one convective ribbon at 28 km shown here compared to many ribbons in R15. This similarity between the reduced planet and full planet 28 km simulations suggests that the reduced planet framework is correctly capturing the physics that manifest in the full-sized, high-resolution configuration. This provides some confidence that further reductions to smaller grid spacings will also capture the model’s behavior at such high resolutions; companion full-sized planet simulations at such resolutions are prohibitively expensive and have not been conducted. While Figure 1 qualitatively suggests differences in precipitation among the five simulations, Figure 2 displays the probability density functions of the 6-hourly averaged total and convective precipitation rates over the final year of each simulation. Here convective precipitation refers to the precipitation that results from the shallow and deep convective parameterizations, while the total precipitation represents the sum of the convective precipitation and that from stratiform processes. Figure 2 also includes the precipitation rates for the equivalent ne120 simulation (gray lines) from R15 and again suggests that the framework consistently captures similar behavior. Specifically, despite a decreased area, the 28 km reduced planet simulation produces a precipitation probability density function that is nearly identical to that for the equivalent ne120 simulation in R15 on a full-sized planet. Similarly, the domain mean total precipitation averaged over the second year of the simulations is about 4.75 mm/d for both configurations, indicating that the mean climates are also similar. The response of total precipitation to decreasing grid spacing is not straightforward. Initially, precipitation rates increase from 111 km to 56 km and then decrease as grid spacing decreases. Convective precipitation rates, on the other hand, experience a systematic decrease with decreasing grid spacing, demonstrating that the precipitation becomes dominated by the resolved-scale processes at the smaller grid spacings. Figure 3 compares the vertical structure of liquid water for the five reduced planet simulations along with the ne120 simulation from R15, divided into ascending (𝜔500 < 0) and descending (𝜔500 > 0) regimes, where 𝜔500 is the vertical pressure velocity at 500 hPa. The division between the regimes is necessary because of the REED AND MEDEIROS
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Figure 3. Mean vertical profiles of daily averaged liquid water content (g kg−1 ) for (left) ascending and (right) descending regions for the second year of each simulation. The classification is simply based on daily mean 𝜔500 . Colors are as in Figure 2. Inward ticks on the vertical axis show the nominal pressure of the model levels.
substantial difference between the moist and dry regions (see Figure 1). In the subsiding regimes, a low-level cloud layer is present in all simulations with a cloud base around 900 hPa; this layer is similar to the model’s representation of the shallow-cumulus-topped trade wind boundary layer in other configurations [e.g., Chandra et al., 2015]. The geometric thickness of this cloud layer is smallest for the 111 km simulation, is similar in thickness for grid spacings of 56 km down to 14 km, and becomes somewhat thicker in the 7 km simulation. The peak liquid water content increases monotonically with decreasing grid spacing down to 14 km and becomes sharply peaked near cloud base; this peak is reduced and distributed through several model levels in the 7 km simulation. The differences in structure are probably the result of differences in the lower tropospheric mixing; it is likely that the 7 km simulation strikes a different balance among resolved mixing, boundary layer turbulence, and shallow convective mixing than the other simulations. All the simulations also show a secondary peak in liquid water content near 600 hPa; this corresponds (roughly) to the freezing/melting level, and there is a similar secondary peak in ice water content at levels slightly above (550 hPa; not shown). It is not clear whether the condensate in this midtropospheric layer in the subsiding regime originates from local occasional deeper convective detrainment or advection from nearby deep convective activity. In the ascending regimes, convection is occurring (both parameterized and resolved). The freezing/melting level features noted in the subsiding regime are more pronounced in the ascending regimes, and the liquid water increases monotonically with decreasing grid spacing throughout the lower troposphere, connected to the stronger upward velocity on smaller scales. As was the case for the distribution of rain rates (Figure 2), the ne120 and 28 km simulations appear very similar in liquid water content profiles in Figure 3, further supporting the notion that the reduced planet framework is mimicking full planet simulations with comparable grid spacing. There is a difference in the vertical distribution of liquid in the 7 and 14 km simulations, which is likely associated with convection being somewhat more persistent in the 14 km case (see supporting information Figure S1). If convective motion brings air into an already nearly saturated environment as in the 14 km simulation in which the convective cluster is nearly stationary, mixing between the ascending and environmental air will not cause much evaporative cooling and consumption of buoyancy, but in the circumstance where the cluster is less stationary, air rising into a dry environment will incur such a penalty and retard the upward motion. In this way, the 7 km simulation may be depositing more moisture at lower levels than the 14 km simulation as it is more likely that any particular updraft is rising into a relatively dry environment. The self-aggregation of convection manifests differently in the simulations. Figure 4 shows a simple diagnostic for aggregation: the fraction of grid points that have mean ascending motion at 500 hPa. At the smaller grid spacings (14 and 7 km), the ascending fraction drops to below 15% in the first months. The 14 km simulation maintains this highly organized state (Figure 1), while the 7 km simulation shows variability but never exceeds the larger grid spacing simulations. The increased variability is consistent with the previous explanation of the liquid water structure. Using 𝜔700 produces very similar results (not shown). The degree of aggregation REED AND MEDEIROS
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Figure 4. Fraction of grid points with ascending midtropospheric vertical motion (i.e., 𝜔500 < 0) from daily averages for each simulation. Colors are as in Figure 2.
may be related to the morphology of the convective clusters in addition to the grid spacing. The simulations that aggregate convection into a single cluster are the 111 km, 14 km, and 7 km simulations, and Figure 4 suggests that the diagnostic is qualitatively measuring the size of the cluster compared to the domain size. The others, including the full-sized planet ne120 simulation in which the diagnostic is much less variable, aggregate convection into ribbons, and all three of them show similar values of this diagnostic, so the surface area covered by the ribbons is rather steady in time no matter the domain size. Whether this is indicative of a feedback process that regulates the size (width and length) of these ribbon-like structures is intriguing, but not clear from the present analysis.
4. Discussion This study leverages the RCE configuration in a global model to probe the effects of reducing grid spacing toward cloud-system-resolving scales. Because planetary rotation is removed, the planetary radius can be reduced without any additional changes in the model physics, making it somewhat simpler than other reduced planet approaches [e.g., Kuang et al., 2005]. By reducing the planetary radius, grid points are drawn together, reducing grid spacing and resolving smaller scales. This provides a means to evaluate the model physics at small grid spacing for the computational cost of a standard climate simulation. The drawback is that the domain size is also reduced, and domain size may be an important aspect of convective aggregation [Muller and Held, 2012; Wing and Emanuel, 2014]. Smaller domains may also have the drawback of not sampling as many convective events, so longer simulations could be required in some situations (though we suspect that is not the case for the results presented here as the simulations are run for 2 years, which is much longer than most CRM simulations). It is worth noting that the number of horizontal grid points used in the global RCE framework presented here (48,602) is within the range of grid points used in previous CRM studies of RCE [e.g., 36,864 in Bretherton et al., 2005 and 65,536 in Wing and Emanuel, 2014]. Ultimately, the value of the reduced planet configuration is determined by the similarity of the reduced planet with the full-sized planet at the equivalent grid spacing. If the two behave similarly, then the advantages of the reduced planet can be reaped. For the pair of 28 km simulations presented here and in R15, there is evidence to suggest that there is similar behavior. Our working hypothesis is that this similarity should hold for the smaller grid spacing, and the 14 and 7 km simulations presented here are representative of tropical marine environments that would be simulated by the full-sized planet at similar grid spacing. Such simulations, either with global high-resolution or regionally refined meshes, are on the horizon. Based on the results reported here, it appears that the representation of convection (including organization of convection) in CAM5 is strongly dependent on grid spacing. The effects of parameterized convection systematically reduce as grid spacing decreases; the resolved motion and grid-scale physics become dominant. As this transition happens, we also find nonmonotonic changes in the structure of clouds, indicating that the balance of processes maintaining the thermodynamic structure changes with grid spacing. Whether these balances are physically plausible remains to be investigated; doing so might entail detailed analysis of the parameterized process rates and possibly comparison to CRM simulations. Such analysis and comparison could also provide additional insight into the mechanisms of the convective aggregation REED AND MEDEIROS
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and whether the different manifestations of organized convection (clusters versus ribbons) are associated with different mechanisms. The reduced complexity RCE framework presented here offers an opportunity to investigate these research questions in the future and aid in the testing of next-generation convection schemes in global models. Acknowledgments The National Center for Atmospheric Research (NCAR) is sponsored by the National Science Foundation. We would like to acknowledge high-performance computing support from Yellowstone (ark:/85065/d7wd3xhc) provided by NCAR’s Computational and Information Systems Laboratory, also sponsored by the National Science Foundation. The model output presented in this study is accessible on Yellowstone. Medeiros was supported by the Regional Climate Modeling Program of the U.S. Department of Energy’s Office of Science (BER), cooperative agreement DE-FC02-97ER62402.
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