PUBLICATIONS. Journal of Advances in Modeling Earth Systems. Simulation of subgrid orographic precipitation with an embedded 2-D cloud-resolving model

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1 PUBLICATIONS Journal of Advances in Modeling Earth Systems RESEARCH ARTICLE /2015MS Key Points: Subgrid orographic precipitation is simulated with an embedded 2-D CRM The simulated mean precipitation is similar to that obtained with 3-D topography Encouraging results suggest the potential of the MMF approach Correspondence to: J.-H. Jung, Citation: Jung, J.-H., and A. Arakawa (2016), Simulation of subgrid orographic precipitation with an embedded 2-D cloud-resolving model, J. Adv. Model. Earth Syst., 8, 31 40, doi: / 2015MS Received 28 AUG 2015 Accepted 14 DEC 2015 Accepted article online 22 DEC 2015 Published online 13 JAN 2016 VC The Authors. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made. Simulation of subgrid orographic precipitation with an embedded 2-D cloud-resolving model Joon-Hee Jung 1 and Akio Arakawa 2 1 Department of Atmospheric Science, Colorado State University, Colorado, USA, 2 Department of Atmospheric and Oceanic Sciences, UCLA, California, USA Abstract By explicitly resolving cloud-scale processes with embedded two-dimensional (2-D) cloudresolving models (CRMs), superparameterized global atmospheric models have successfully simulated various atmospheric events over a wide range of time scales. Up to now, however, such models have not included the effects of topography on the CRM grid scale. We have used both 3-D and 2-D CRMs to simulate the effects of topography with prescribed large-scale winds. The 3-D CRM is used as a benchmark. The results show that the mean precipitation can be simulated reasonably well by using a 2-D representation of topography as long as the statistics of the topography such as the mean and standard deviation are closely represented. It is also shown that the use of a set of two perpendicular 2-D grids can significantly reduce the error due to a 2-D representation of topography. 1. Introduction General circulation models (GCMs) must be able to represent orographic precipitation in order to properly simulate the local weather and climate in and around mountainous areas. For a review of the orographic effects on weather and climate, see, e.g., Beniston et al. [1997] and Chow et al. [2013]. Studies have shown that the horizontal grid spacing required for simulating realistic orographic precipitation is smaller than 5 km [e.g., Colle and Mass, 2000]. That is why high-resolution mesoscale models are commonly used to study weather systems with the orographic precipitation [e.g., Colle and Mass, 1996; Colle, 2004; Yang and Chen, 2008; Barrett et al., 2009; Watson and Lane, 2012, 2014]. Given that such high resolution is not practical for GCMs in the foreseeable future, alternative methods are needed to represent orographic precipitation in GCMs. Leung and Ghan [1995, 1998] proposed a parameterization of subgrid-scale orographic precipitation for use in GCMs. In their parameterization, the subgrid variations of surface elevation are aggregated to define a limited number of elevation classes. For each elevation class, a simple airflow model determines the orographic ascent or descent of the air, and a thermodynamic model uses that information to diagnose the cloud properties. For each GCM grid cell, these results are combined according to the distribution of elevation. They showed that with this parameterization the Pacific Northwest National Laboratory s Regional Climate Model (PNNL-RCM) yields more realistic spatial distributions of precipitation and snow cover in mountainous regions. Also, they showed that the simulation of the regional mean surface temperature over the western United States can be improved by using this parameterization combined with a subgrid vegetation scheme. From their work, it is proven that the subgrid-scale orographic precipitation should be represented in climate models and it can be done by the parameterization. Despite its practical merits, the parameterization approach has inherent limitations due to a number of idealizations. As an alternative path to treat unresolved subgrid-scale processes in GCMs, a new approach called the Multiscale Modeling Framework (MMF) has been recently developed. In this approach, the traditional subgrid-scale parameterizations in the GCMs are replaced with explicit simulations by a 2-D cloudresolving model (CRM) embedded in each GCM grid column [Grabowski and Smolarkiewicz, 1999; Randall et al., 2003]. The embedded CRM is called a superparameterization. The justification for using 2-D CRMs is that they are reasonably successful in simulating the gross thermodynamic effects of deep moist convection [e.g., Grabowski et al., 1998; Xu et al., 2002]. MMFs are much more computationally expensive than conventional GCMs but they take advantage of the rapid progress in the parallel supercomputing resources. The MMFs developed so far have shown JUNG AND ARAKAWA SUBGRID OROGRAPHIC PRECIPITATION 31

2 Figure 1. Schematic illustration of the horizontal grid structures of (a) 3D MMF, (b) 2D MMF-X, and (c) 2D MMF-Y. substantial improvements in simulating various atmospheric events over a wide range of time scales [e.g., Khairoutdinov et al., 2005; Ovtchinnikov et al., 2006; Khairoutdinov et al., 2008; Benedict and Randall, 2009; Tao et al., 2009; Stan et al., 2010; DeMott et al., 2011; Pritchard et al., 2011; Xu and Cheng, 2013; Krishnamurthy et al., 2014]. In the MMF approach, the effects of subgrid orography on clouds and precipitation can be explicitly resolved by the embedded CRMs. In this way, the subgrid orographic effects can be directly coupled with various atmospheric processes of larger scales. This has not been attempted yet, but it is especially important because precipitation over and near mountains mostly occurs when storms form near or move over complex terrain, as Houze [2012] pointed out. Also, in this approach, the rain shadowing effect on the lee side of mountains can be explicitly resolved by the embedded CRMs, at least partially, depending on how topography is represented. This is one of the major differences from the parameterization of Leung and Ghan [1995, 1998]. In their elevation-class scheme that carries no information on the spatial distribution of topography within each GCM grid cell, the subgrid-scale rain shadowing effect cannot be represented. Despite of potential merits of the MMF approach in the simulation of the orographic precipitation, the subgridscale inhomogeneity in topography has not been yet incorporated to the current-generation MMFs developed so far. For future application, we must ask whether it is really acceptable to use a 2-D CRM to simulate orographic precipitation due to complex 3-D topography, even statistically. The purpose of this paper is to answer that question. The paper is organized as follows. Section 2 describes the experimental strategy using an idealized MMF, in which a 2-D or a 3-D CRM is embedded in a single-column inactive GCM. The characteristics of the model and the simulation conditions including the surface elevation data are also described in section 2. The simulated statistics of orographic precipitation are presented in section 3. The paper ends with summary and concluding remarks in section Simulation Design 2.1. Basic Strategy To see the impact of the 2-D representation of 3-D topography on precipitation, we adopt an approach that mimics an MMF but without unnecessary complications. The simulations of subgrid orographic precipitation are performed with a single-column inactive GCM, using either a 3-D or 2-D cloud-resolving model (CRM) as a superparameterization. Even though this model is not a global GCM, the main idea of MMF approach is still fully implanted. Thus, we call this model 3D MMF or 2D MMF, respectively, depending on the dimensionality of the CRM used. Figure 1 illustrates the horizontal grid structures of the 3-D MMF and the 2-D MMF. As shown in Figures 1b and 1c, the 2-D CRM is oriented in the x and y directions, respectively, to create 2-D MMF-X and 2-D MMF-Y. In these MMFs, the CRM explicitly simulates development of deep convection over mountains and associated precipitation inside the GCM column. The horizontal cell size of the GCM is chosen to be a typical grid size of today s coarse-resolution GCMs. Vertical profiles of horizontally uniform thermodynamic state and horizontal flow are prescribed. It is assumed that these profiles are maintained with time by large-scale processes such as heat and moisture advection. The predicted thermodynamic state and horizontal flow of the CRM, averaged over the whole domain, are nudged to those of the GCM. This mimics the influence of the GCM on the embedded CRM component in an MMF, and maintains active convection in the CRM against the drying effects of convection. JUNG AND ARAKAWA SUBGRID OROGRAPHIC PRECIPITATION 32

3 To examine how well the statistics of subgrid orographic precipitation can be simulated with a 2-D representation of complex 3-D topography, simulations have been performed using the 3-D and 2-D MMFs with a variety of surface elevation data, and the resulting precipitation statistics have been compared. We assume that the 3-D MMF provides a true solution or benchmark Model and Simulation Conditions The Vector-Vorticity Model (VVM) is used for the CRM component of the idealized MMF. The original VVM is a 3-D nonhydrostatic anelastic model developed by Jung and Arakawa [2008], with a unique dynamical core based on the 3-D vorticity equation. In the VVM, the anelastic approximation is implemented by solving a 3-D elliptic equation for vertical velocity. (This contrasts with anelastic models based on the momentum equation, in which the elliptic equation is solved for the pressure.) Solution for the vertical velocity simplifies the formulation of the lower boundary condition for the elliptic equation with surface topography, as shown by Wu and Arakawa [2011]. The horizontal velocity components are diagnosed from the components of the horizontal vorticity. The physical parameterizations of the model include a three-phase bulk microphysics parameterization [Lin et al., 1983; Lord et al., 1984; Krueger et al., 1995], the RRTMG longwave and shortwave radiation parameterization [Iacono et al., 2008], and a first-order turbulence closure that uses eddy viscosity and diffusivity coefficients depending on deformation and stability [Shutts and Gray, 1994]. The VVM has previously been applied in a variety of studies [e.g., Jung and Arakawa, 2010, 2014; Jones and Randall, 2011; Wu and Arakawa, 2011; Arakawa and Wu, 2013; Wu and Arakawa, 2014]. For this study, surface topography has been implemented in the VVM following the block-mountain method of Wu and Arakawa [2011]. The 2-D and 3-D versions of this VVM are used for the 2D and 3D MMFs, respectively. The horizontal and vertical domain sizes of the single-column GCM are 300 km km and 30 km, respectively. For the thermodynamic state of the GCM, the vertical profiles of potential temperature h and moisture q are prescribed similar to the environmental soundings employed by Weisman and Klemp [1982]: 8 h ðþ5 z z 5=4 >< h 0 1ðh tr 2h 0 Þ ; z tr z z tr g >: h tr exp ðz2z tr Þ ; c p T tr z > z tr q ðþ5 z ( H ðþq z ðþ; z q z5ztr ; z z tr z > z tr where z tr 5 12 km, h tr K, and T tr K represent the height, potential temperature, and temperature, respectively, at the tropopause, h K is the surface potential temperature, q is the saturated mixing ratio and H is the relative humidity given by H ðþ512 z 3 z 5=4 : (3) 4 All other water species (cloud water and ice, snow and graupel) are initially set to zero. The winds are set to a uniform southwesterly flow with u5v510 m s 21. For the 3-D MMF runs, the CRM uses the same horizontal domain as the GCM, as illustrated in Figure 1a, while it covers only one cross section in xz plane (Figure 1b) or yz plane (Figure 1c) for the 2-D MMF runs. The horizontal grid spacing of the CRM is 3 km. There are 34 layers in the vertical, using a stretched grid with a vertical grid spacing ranging from about 0.1 km near the surface to about 1.7 km near the model top. In the vertical, the CRM and the single-column GCM share the same grid. The upper and lower boundaries are rigid surfaces. Rayleigh-damping is applied in the uppermost 10 km, in order to absorb upwardpropagating waves. The lateral boundaries are doubly periodic. For simplicity, the Coriolis acceleration, radiation, and the surface fluxes of sensible heat and moisture are not included in the simulation. For the 3-D MMF runs, the CRM simulation starts from the horizontally uniform GCM state except near mountain surfaces, where local flows are calculated using the block mountain method. For the 2-D MMF runs, the CRM simulation starts from a selected cross section of the initial state of the 3-D run, z tr (1) (2) JUNG AND ARAKAWA SUBGRID OROGRAPHIC PRECIPITATION 33

4 Figure 2. Surface elevation data for 15 selected cases used in the simulations. SD denotes the standard deviations. JUNG AND ARAKAWA SUBGRID OROGRAPHIC PRECIPITATION 34

5 Figure 3. Horizontal distributions of the mean intensity of surface precipitation simulated by the idealized 3-D MMF. The contour interval is 5 mm h 21. The surface elevations are shaded, which are same as in Figure 2. JUNG AND ARAKAWA SUBGRID OROGRAPHIC PRECIPITATION 35

6 Normalized surface precipitation intensity CASE Figure 4. Normalized mean intensities of surface precipitation obtained from the results of 15 simulations by the 3-D MMF. The mean values are calculated during the last 24 h simulation period over the GCM-cell domain. For the detail of normalization, see the text. corresponding to the location of its 2-D domain. Throughout the simulation, the CRM domain averages of the thermodynamic state and the horizontal flow are nudged to those of the single-column GCM, with a 1-h time scale. Each simulation is integrated for 48 h, using 10 s for the time step of the CRM Surface Elevation Data Simulation of the surface precipitation can be very sensitive to the statistics of the surface elevation and, therefore, the effects of a variety of terrain shapes need to be examined in order to reach a general conclusion. Since it is almost impossible to parametrically represent complex multiscale terrain characteristics with sufficient generality, we have decided to use samples from high-resolution data for the real surface topography. Fifteen sets of surface elevation data are randomly selected from 1 min grid data of the American Rockies, Alps, and Andes [Smith and Sandwell, 1997]. To accommodate the cyclic horizontal boundary conditions used in the model, the original surface elevation h in the data is replaced by h given by: where Cx ðþis a correction term given by D is the domain size in the x direction and h ðþ5max x f0:; ½hx ðþ1cðþ xšg (4) Cx ðþcð0þcos ðpx=dþ; (5) Cð0Þ5½hð0Þ1hðDÞŠ=22hð0Þ: (6) The same procedure is also applied in the y direction. In this way, the surface elevation data satisfy the doubly cyclic boundary conditions. In order to focus on the influence of subgrid-scale variations of the surface elevation on the precipitation, the domain averages of the surface elevation for all 15 cases are adjusted to 1 km by applying a constant multiplicative factor F chosen for each case as follows: N H 0 F5 X h ðx; yþ=n (7) where H 0 is a given height (1 km) and N is the number of data used. Figure 2 shows 15 surface elevation data sets prepared with the modifications described above. We see from the figure that, although the domain-averaged magnitude is the same, the individual cases differ significantly from each other both in the standard deviation and characteristic shape. 3. Simulation Results For each case shown in Figure 2, we performed a 48 h simulation with the 3-D MMF, the 2-D MMF-X, and the 2- D MMF-Y. For most cases, it is observed from the evolution of domain-averaged precipitation that an approximate steady state is achieved after 6 to 10 h of integration (not shown). The results of the last 24 h of each simulation are presented in this section CASE Figure 5. The standard deviations of surface elevation normalized by the value of Case Precipitation Simulated by the 3-D MMF Figure 3 presents the horizontal distributions of the mean intensity of surface precipitation, as simulated by the 3-D MMF. The mean is calculated over the 24 h period selected for the analysis of results. JUNG AND ARAKAWA SUBGRID OROGRAPHIC PRECIPITATION 36

7 From the figure, it can be seen that the distributions of orographic precipitation inside the GCM cell are quite different between the cases. As well documented by Houze [2012], there are various mechanisms to generate or enhance precipitation over and near mountains. Without preexisting weather systems such as storms, fronts, and tropical cyclones, however, the main forcing mechanism contributing to the generation of precipitation is simply upslope lifting on the windward sides of mountains. In the simulations shown in Figure 3, the nonlinear interactions between the encountering moist airflow and the mountains with different heights and shapes result in diverse distributions of precipitation even though the environmental conditions are almost same. The complexity of mountains makes it difficult to predict the favored precipitation pattern inside the GCM cell. Nevertheless, heavy precipitation in the windward side and rain shadowing effect in the lee side against the southwesterly mean wind are still observed from many cases. Since we are primarily interested in the precipitation recognized by the GCM, the intensity of surface precipitation is averaged over the GCM grid-cell. The results for all 15 cases are shown in Figure 4. In this figure, the mean precipitation intensities are normalized by the precipitation intensity simulated with a flat topography of 1 km height. (For the flat-topography simulation, a random perturbation is applied to the potential temperature field at the lowest model layer for the first 10 min of simulation to initiate convection.) This figure clearly shows that the surface precipitation intensity generally increases due to the subgrid-scale inhomogeneity in topography. Figure 5 presents the standard deviations of surface elevation normalized by the value for Case 2, which is the smallest among all of the cases. Comparison between Figures 4 and 5 shows that the increase of mean precipitation intensity due to the subgrid-scale inhomogeneity in topography is very closely correlated with the standard deviation of the topography. We see from Figures 4 and 5 that both the surface precipitation and the standard deviation of surface elevation are large for cases 3, 7, 8, 10, and 11. Figure 2 shows that the cases with large standard deviations are characterized by pronounced mesoscale ridges, and thus we may say that the subgrid precipitation is primarily associated with those ridges. This rather simple result is more than expected from the complexity in the precipitation pattern shown in Figure 3. This may suggest that the problem of determining the domain-averaged precipitation can be separated from that of determining the precipitation pattern D Simulations Versus 2-D Simulations Encouraged by the relatively simple results for the domain-averaged precipitation presented above, we now investigate how well the 2-D MMFs can reproduce the results from the 3-D MMF. As an example, Figure 6 shows the surface elevation data of Case 3 for the 3-D MMF, 2-D MMF-X, and 2-D MMF-Y. As shown in the figure, the 2-D CRM recognizes only a cross section of the complex 3-D topography depending on the location of the 2-D CRM inside the GCM grid cell. In addition, the mean heights of topography recognized by the 2-D MMFs are generally different from that of the 3-D MMF. To eliminate this difference due to the sampling of 2-D grid, we adjust the mean height for each 2-D MMF to that for the 3-D MMF by applying a constant multiplicative factor. This is an important procedure that should be remembered in future practical applications of our approach. The precipitation statistics simulated by the 3-D and 2-D MMFs are compared in Figure 7. This figure presents the horizontal domain averages of mean surface precipitation normalized by the reference value simulated by the 3-D MMF with a flat topography of 1 km height. The 3-D MMF results are the same as those shown in Figure 4. Figures 7a and 7b show that the simulated results from the 2-D MMFs are similar to those of the 3-D MMF in most cases. However, there are cases (3, 7) in which the results of the 3-D and each 2-D MMF are significantly different. Even for these cases, we see that the differences from the 3-D MMF are considerably reduced by averaging the results of the two 2-D MMFs (Figure 7c). The implications of these encouraging results are discussed in the next section. 4. Summary and Discussion To demonstrate how well a 2-D representation of topography can simulate the precipitation statistics due to complex 3-D topography, simulations have been performed with single-column 3-D and 2-D MMFs, using a variety of surface elevation data. Comparisons of the results confirm that the 2-D representation of topography in the 2-D MMFs can simulate the surface precipitation averaged over the GCM grid cell reasonably well, as long as the topographic statistics, such as the mean and standard deviation of the surface elevation, JUNG AND ARAKAWA SUBGRID OROGRAPHIC PRECIPITATION 37

8 Figure 6. Examples of the surface elevation data (Case 3) as represented in (a) 3-D MMF, (b) 2-D MMF-X, and (c) 2-D MMF-Y. Figure 7. As in Figure 4, except that (a) the results of 2-D MMF-X, (b) the results of 2-D MMF-Y, and (c) the averages of the two are added to those of 3-D MMF (black). JUNG AND ARAKAWA SUBGRID OROGRAPHIC PRECIPITATION 38

9 are closely represented. Although it is not always true that a single 2-D CRM can capture the effects of 3-D topography, the use of two 2-D CRMs oriented perpendicularly to each other can significantly reduce the error in the surface precipitation due to a single 2-D representation of the topography. The results of this study are encouraging in the sense that they show the strong potential of the MMF approach for simulating the total subgrid orographic precipitation in a grid cell. The success with the 2-D representation of topography must be partly due to the fact that the total precipitation is nearly proportional to the standard deviation of surface elevation as shown in Figures 4 and 5, and partly because the standard deviations recognized by the 2-D MMFs are generally very similar to those recognized by the 3-D MMF (not shown). It should be remembered, however, that the coefficient of proportionality between the total precipitation and the standard deviation of surface elevation can be a complex function of various environmental factors, including the direction and magnitude of the background flow, which control the forced topographical ascent/descent, and the vertical and horizontal structures of temperature and humidity, which control the overall convective response to the ascent/descent. The main modeling problem is to effectively determine such a function for a given realization of the environmental factors. In the MMF approach, the convective effects are estimated directly from the statistics of convective activity as explicitly simulated by a 2-D CRM embedded in each GCM grid cell. Therefore, in this framework, the complex function mentioned above does not have to be parameterized since it can be directly evaluated by the CRM. However, the use of purely a 2-D CRM in the MMF has limitations in predicting the associated wind field. Also, the cyclic lateral boundary conditions applied to the CRMs make it difficult to represent subgrid-scale topography. To overcome these problems, Jung and Arakawa [2010, 2014] proposed a new generation of MMF called the quasi-3-d multiscale modeling framework (Q3-D MMF), by introducing the following modifications to the current-generation MMF: (1) The CRMs are extended beyond the GCM grid columns, eliminating the cyclic lateral boundary conditions; (2) The 2-D CRMs are replaced with 3-D CRMs applied to narrow horizontal channel-domains; and (3) Two perpendicular sets of CRMs are used. Due to the first modification mentioned above, the Q3-D MMF is able to fully represent the subgrid-scale inhomogeneity along the channel direction. (In terms of the horizontal grid structure, this is similar to the combination of 2-D MMF-X and 2-D MMF-Y in Figure 1.) The Q3-D MMF can also improve the prediction of wind field due to the modifications (2) and (3), as shown in Jung and Arakawa [2014]. With these modifications, the Q3-D MMF is expected to produce an overall improvement in the simulation of orographic effects on clouds and precipitation. However, the improvement comes with an increase of computational cost, especially due to the elimination of the cyclic lateral boundary conditions of the embedded CRMs. It remains to fully optimize the algorithm of the Q3-D MMF for affordable global calculations. Full evaluation of the Q3-D MMF with steep topography using an interactive GCM is in progress and will be reported elsewhere. Acknowledgments We thank Dave Randall for his suggestions to improve the original manuscript. We also thank Mike Pritchard and two anonymous reviewers for their helpful comments. 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