9.4 SILHS: A MONTE CARLO INTERFACE BETWEEN CLOUDS AND MICROPHYSICS

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1 9.4 SILHS: A MONTE CARLO INTERFACE BETWEEN CLOUDS AND MICROPHYSICS Vincent E. Larson, Carsten Harlass, and Jan Höft Dept. of Mathematical Sciences, University of Wisconsin Milwaukee, Milwaukee, WI 1. INTRODUCTION Clouds exhibit spatial variability on a range of scales, and this variability influences microphysical processes such as drizzle formation (Pincus and Klein 2000; Larson et al. 2001). For this and other reasons, large-scale models may benefit from including the effects of subgrid cloud variability on microphysical process rates. For instance, feeding the fraction of a grid box occupied by cloud into a microphysics parameterization may help better characterize the moist parts of a grid box in which drizzle forms. Accuracy may also be improved by including information on within-cloud variability. Unfortunately, embedding information about subgrid cloud variability in microphysics schemes is laborious. In a model such as the Weather Research and Forecasting (WRF) model, which contains many microphysics schemes, embedding subgrid information separately in each microphysics scheme would be especially time consuming. In this paper, we test an alternative Monte Carlo method of driving microphysics schemes with information about subgrid variability. The method assumes that the distribution of subgrid variability is available for each grid box and time step. It then draws samples from that distribution. The sample points are fed, one by one, into the microphysics scheme in use. Finally, the process rates from each call to the microphysics are averaged and fed back into the simulation. This Monte Carlo metholodogy is related to the McICA method which has been used to drive radiative parameterizations (e.g. Barker et al. 2002; Pincus et al. 2003; Räisänen et al. 2004; Räisänen and Barker 2004; Räisänen et al. 2005; Pincus et al. 2006). For reasons to be discussed below, we call this method the Subgrid Importance Latin Hypercube Sampler (SILHS). SILHS separates the calculation of subgrid variability and the calculation of local microphysical process rates. Because of this, SILHS can include effects of subgrid variability without requiring modifications to the microphysics code itself. We test SILHS by performing month-long, 3D simulations of marine low clouds off the coast of Chile. These clouds were observed during the VAMOS Ocean-Cloud-Atmosphere-Land Study Regional Experiment (VOCALS-REx) (Wood et al. 2011). We find that the use of SILHS noticeably increases cloud cover. Corresponding author address: Vincent E. Larson, Department of Mathematical Sciences, University of Wisconsin Milwaukee, P. O. Box 413, Milwaukee, WI , vlarson at uwm dot edu, vlarson. This paper is organized as follows. We first summarize SILHS formulation and usage in Section 2. Then we test SILHS in simulations of VOCALS observations (Section 3.). Finally, we summarize our findings in Section DESCRIPTION OF OUR MONTE CARLO SAMPLER, SILHS SILHS job is to take a particular piece of information about subgrid variability, namely a subgrid probability density function (PDF), and draw an unbiased sample from the PDF. In other words, SILHS input is a subgrid PDF, and its output is a set of sample points. In order for SILHS to function within a large-scale host model such as WRF, SILHS needs to be provided a subgrid PDF for each grid box and time step. In our simulations, the subgrid PDF is predicted for each grid box and time step by the Cloud Layers Unified By Binormals (CLUBB) parameterization (Golaz et al. 2002; Larson and Golaz 2005; Larson et al. 2012). CLUBB s PDF is a joint PDF of momentum, heat content, moisture, and hydrometeors. SILHS also requires code to feed SILHS samples into a microphysics scheme and average the results. SILHS role within WRF-CLUBB may be summarized by the following four steps, which must be carried out for each grid column and time step (see Larson and Schanen (2013) for more detail): 1. Predict a subgrid PDF (handled by CLUBB). CLUBB s PDF is a joint PDF of momentum, heat content, moisture, and hydrometeors. CLUBB predicts the PDF by prognosing some relevant moments using higher-order closure equations and diagnosing other moments. CLUBB assumes that the marginal PDFs are distributed according to a sum of two normal distributions for dynamical or thermodynamical quantities or else a single lognormal distribution for hydrometeors. Correlations are prescribed in these simulations, although Larson et al. (2011) have proposed an approximate method to diagnose correlations. Since a subgrid PDF is predicted for each vertical level, CLUBB predicts a column of overlying PDFs. 2. Draw sample points from the subgrid PDF (handled by SILHS). Given a subgrid PDF provided by CLUBB, SILHS draws a user-specified number of sample points from it. The sample points from a grid column of overlying grid boxes are chosen such as to form vertical profiles of samples. These sampled vertical profiles (or subcolumns ) can

2 be specified to have a desired degree of coherence in the vertical. In order to reduce statistical noise from the use of small samples, SILHS uses two variance reduction techniques. First, SILHS preferentially draws sample points from an important region, namely liquid cloud. Second, in order to avoid clumping of sample points, SILHS attempts to spread out sample points by using Latin hypercube sampling (McKay et al. 1979; Press et al. 1992; Owen 2003; Gentle 2003; Larson et al. 2005). The fact that SILHS uses both importance and Latin hypercube sampling is what inspired SILHS name. 3. Feed sample points, one by one, into a microphysics scheme. Each vertical profile of sample points, from each grid column and time step, is fed one at a time into a microphysics scheme. The microphysics scheme does not know that the profiles originate from a sample; the microphysics scheme computes tendencies on the assumption that the profile is horizontally uniform within an individual subcolumn. 4. Average microphysical tendencies to form a grid box average. The sample microphysical process rates are averaged using a weighted average that accounts for SILHS importance sampling. The resulting estimate of the grid box average is fed back into the host model, namely WRF. The steps are then repeated. We have implemented SILHS in a private copy of WRF-CLUBB. 3. EVALUATION OF WRF-CLUBB-SILHS: A SIMULATION OF MARINE LOW CLOUDS 3.1 Cloud case that we simulate: VOCA As a test case, we simulate the VOCA model intercomparison case led by M. Wyant. VOCA is a follow up to the PreVOCA intercomparison (Wyant et al. 2010). VOCA is a regional simulation of the VOCALS observations of marine Sc off the coast of Chile. This marine Sc deck is vast, and it is important because it reflects shortwave radiation and hence cools the climate. VOCA also serves as a difficult test of numerical models because it contains several cloud types, including decoupled stratocumulus and deep cumulus clouds over the Amazon. The VOCA simulation includes the full observational period from 15 Oct 2008 to 15 Nov The case specification is described at /model/voca Model Spec.htm. 3.2 Model configuration The WRF-CLUBB simulations reported here are based upon version of the Advanced Research WRF model. The vertical grid uses 45 levels, with refined grid spacing in the boundary layer. The horizontal grid spacing is 100 km for coarse resolution simulations and 25 km for finer resolution simulations. The timestep is 60 s for both WRF and CLUBB. To represent microphysics, we use the Morrison ( M ) double-moment scheme (Morrison et al. 2009). Our simulation contains no aerosol-cloud interactions or chemistry computations. We impose a constant cloud droplet number concentration of 150 cm 3. To represent radiative transfer, we use the RRTM longwave (Mlawer et al. 1997) and the Dudhia shortwave (Dudhia 1989) parameterizations. The initial and lateral boundary conditions are derived from the NCEP2 reanalysis dataset. The model domain spans approximately -45 S to 5 N and from W to -60 W. The grid projection is Mercator. 3.3 Simulated and observed cloud cover Figure 1 displays cloud cover, i.e. the frequency of cloud occurrence. The MODIS satellite observations (panel f) show overcast clouds near the coast at 20 S and another maximum of cloud fraction near 40 S. WRF-CLUBB simulations at 100-km horizontal grid spacing without SILHS (panel a) differ from the observations in two notable ways. First, WRF-CLUBB s maximum of cloud cover lies too far to the north, at 10 S instead of 20 S. Second, WRF-CLUBB underpredicts cloud cover overall. Including 2 SILHS sample points per grid box and time step in the 100-km simulation (panel b) does not fix the misplacement of the cloud deck, but it does increase the overall cloud cover, improving the agreement with observations. We speculate that the underestimation of cloud cover when SILHS is omitted occurs because of the use of saturation adjustment on grid mean properties. The M microphysics uses saturation adjustment in order to diagnose liquid water and water vapor. If a grid box is subsaturated in the mean, then the M microphysics will instantaneously evaporate any liquid present. This spuriously evaporates subgrid cumulus clouds that exist in a dry environment with a subsaturated grid mean. The use of only 2 sample points per grid box and time step yields a noisy instantaneous sample (Larson et al. 2005; Larson and Schanen 2013). Does increasing the number of sample points improve the results? Surprisingly, we find that when the number of sample points is increased from 2 to 16, with no other modifications to the code or configuration, the time-averaged results change little (compare panels b and c). Although the instantaneous noise is reduced when 16 sample points are used, a month-long average, as shown in panels b and c, exhibits little difference. This suggests that when time-average quantities are of primary interest, even as few as 2 sample points may be adequate. A grid spacing of 100 km is coarse by today s standards. At finer resolutions, more clouds are resolved, and we would expect subgrid parameterizations to be less influential. Does the use of SILHS still have an ap-

3 Figure 1: Cloud cover as simulated by WRF-CLUBB and observed by satellite during the VOCALS experiment, Oct 15 Nov : a) WRF-CLUBB simulation with 100-km horizontal grid spacing and without SILHS; b) a 100-km simulation with 2 SILHS sample points per grid box and time step; c) a 100-km simulation with 16 SILHS sample points; d) a 25-km simulation without SILHS; e) a 25-km simulation with 2 SILHS sample points; and f) observed cloud cover over the VOCALS region (courtesy R. Wood and M. Wyant), using the mean (10:30am local time) total cloud cover from MODIS on the NASA Terra Satellite Oct 15-Nov 15th 2008.

4 Table 1: Relative computational expense of WRF- CLUBB simulations without SILHS, with SILHS using 2 sample points per grid box and time steps, and with SILHS using 16 sample points. Relative Model configuration computational expense WRF-CLUBB, no SILHS 1.0 WRF-CLUBB, 2 SILHS points 1.2 WRF-CLUBB, 16 SILHS points 3.1 preciable effect when a finer resolution is used? When we test a finer horizontal grid spacing of 25 km, we find that the use of SILHS still significantly increases cloud cover (panels d and e). We have not explored even finer resolutions due to computational constraints. 3.4 Computational cost of SILHS Using SILHS is computationally expensive for several reasons (Larson and Schanen 2013). The most obvious added expense is computing microphysics multiple times per grid box and time step. In addition, SILHS itself is expensive for at least two reasons. First, since SILHS assumes that the PDFs are normal or lognormal, expensive transformations using mathematical special functions need to be performed between the uniformly distributed points generated by a random number generator and points distributed normally or lognormally. Second, because SILHS is multivariate, a transformation needs to be made between the independent multivariate samples and correlated multivariate samples. Nevertheless, when only two sample points are used per grid box and time step, the extra computational cost is only 20% (see Table 1). It is possible that the speed could be increased by optimizing the code, parallelizing the algorithm, or using more efficient integration techniques. 4. CONCLUSIONS SILHS is a Monte Carlo method to drive a microphysics scheme in a large-scale model using subgrid variability. SILHS samples a PDF of subgrid variability and feeds the sample points into a microphysics parameterization. We have implemented SILHS in WRF and used the combined model in order to simulate marine low clouds observed during the VOCALS field experiment. To summarize, we now list some of our key findings: One disadvantage of SILHS is that it introduces statistical sampling noise into simulations. However, we find that even with only 2 sample points per grid box and time step, the noise injected by SILHS is not apparent in monthly averages of shallow cloud cover. Another disadvantage of SILHS is that it is computationally expensive. However, adequate sampling can be obtained with only 2 sample points per grid box and timestep, and in this configuration, the use of SILHS increases the computational cost of WRF-CLUBB simulations by only 20%. One advantage of SILHS is that it separates the calculation of subgrid variability from the calculation of microphysical process rates themselves. Because of this, SILHS requires no modification of the microphysics scheme itself. The non-intrusive nature of SILHS facilitates the introduction of subgrid variability into microphysics schemes. With further development, SILHS might serve as a convenient and general interface between subgrid variability in WRF and the many microphysics options in WRF. A further advantage of SILHS over less expensive samplers is that SILHS is multivariate. This allows SILHS to represent processes involving multiple hydrometeors, such as the accretion of cloud droplets by raindrops. The use of SILHS in simulations of VOCA increases low cloud cover. The increase appears to occur because, with SILHS, subgrid cumulus clouds in subsaturated grid boxes are no longer spuriously evaporated by saturation adjustment in the microphysics. It is possible to conceive of generalizing SILHS, in the future, to drive non-microphysical processes, such as radiation or atmospheric chemistry. In this way, the same representation of subgrid variability could be fed to multiple physics parameterizations, thereby increasing the consistency of large-scale models. 5. ACKNOWLEDGMENTS The authors are grateful for financial support provided by Grant AGS from the National Science Foundation, Grant DE-SC of the U.S. Department of Energy, and by the visitor program of the Developmental Testbed Center at the National Center for Atmospheric Research. The authors thank Matt Wyant and Rob Wood for providing the observational figure. References Barker, H. W., R. Pincus, and J.-J. Morcrette, 2002: The Monte Carlo Independent Column Approximation: Application within large-scale models. Proceedings of the GCSS workshop, Kananaskis, Alberta, Canada, Amer. Meteor. Soc. Dudhia, J., 1989: Numerical study of convection observed during the winter monsoon experiment using a mesoscale two-dimensional model. J. Atmos. Sci., 46,

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