Anisotropy of Observed and Simulated Turbulence in Marine Stratocumulus

Abstract

Anisotropy of turbulence near the top of the stratocumulus-topped boundary layer (STBL) is studied using large-eddy simulation (LES) and measurements from the POST and DYCOMS-II field campaigns. Focusing on turbulence $\sim 100$ m below the cloud top, we see remarkable similarity between daytime and nocturnal flight data covering different inversion strengths and free-tropospheric conditions. With λ denoting wavelength and $z_{\mathrm{t}}$ cloud-top height, we find that turbulence at $\lambda /z_{\mathrm{t}}\simeq 0.01$ is weakly dominated by horizontal fluctuations, while turbulence at $\lambda /z_{\mathrm{t}}>1$ becomes strongly dominated by horizontal fluctuations. Between are scales at which vertical fluctuations dominate. Typical-resolution LES of the STBL (based on POST flight 13 and DYCOMS-II flight 1) captures observed characteristics of below-cloud-top turbulence reasonably well. However, using a fixed vertical grid spacing of 5 m, decreasing the horizontal grid spacing and increasing the subgrid-scale mixing length leads to increased dominance of vertical fluctuations, increased entrainment velocity, and decreased liquid water path. Our analysis supports the notion that entrainment parameterizations (e.g., in climate models) could potentially be improved by accounting more accurately for anisotropic deformation of turbulence in the cloud-top region. While LES has the potential to facilitate improved understanding of anisotropic cloud-top turbulence, sensitivity to grid spacing, grid-box aspect ratio, and subgrid-scale model needs to be addressed.

References Agee, E. M., Chen, T. S., & Dowell, K. E. (1973). A review of mesoscale cellular convection. Bulletin of the American Meteorological Society, 54, 1004–1012. https://doi.org/10.1175/1520-0477(1973)054<1004:AROMCC>2.0.CO;2 Caughey, S. J., Crease, B. A., & Roach, W. T. (1982). A field study of nocturnal stratocumulus II turbulence structure and entrainment. Quarterly Journal of the Royal Meteorological Society, 108, 125–144. https://doi.org/10.1002/qj.49710845508 Cheng, A., Xu, K.-M., & Stevens, B. (2010). Effects of resolution on the simulation of boundary-layer clouds and the partition of kinetic energy to subgrid scales. Journal of Advances in Modeling Earth Systems, 2, 3. https://doi.org/10.3894/JAMES.2010.2.3 Chung, D., & Matheou, G. (2014). Large-eddy simulation of stratified turbulence. Part I: A vortex-based subgrid-scale model. Journal of the Atmospheric Sciences, 71, 1863–1879. https://doi.org/10.1175/JAS-D-13-0126.1 Clark, T. L., & Farley, R. D. (1984). Severe downslope windstorm calculations in two and three spatial dimensions using anelastic interactive grid nesting: A possible mechanism for gustiness. Journal of the Atmospheric Sciences, 41, 329–350. https://doi.org/10.1175/1520-0469(1984)041<0329:SDWCIT>2.0.CO;2 Deardorff, J. W. (1980). Stratocumulus-capped mixed layers derived from a three-dimensional model. Boundary-Layer Meteorology, 18, 495–527. https://doi.org/10.1007/BF00119502 de Lozar, A., & Mellado, J. P. (2013). Direct numerical simulations of a smoke cloud-top mixing layer as a model for stratocumuli. Journal of the Atmospheric Sciences, 70, 2356–2375. https://doi.org/10.1175/JAS-D-12-0333.1 de Lozar, A., & Mellado, J. P. (2015). Mixing driven by radiative and evaporative cooling at the stratocumulus top. Journal of the Atmospheric Sciences, 72, 4681–4700. https://doi.org/10.1175/JAS-D-15-0087.1 de Roode, S. R., Duynkerke, P. G., & Jonker, H. J. (2004). Large-eddy simulation: How large is large enough? Journal of the Atmospheric Sciences, 61, 403–421. https://doi.org/10.1175/1520-0469(2004)061<0403:LSHLIL>2.0.CO;2 Gerber, H., Frick, G., Malinowski, S. P., Brenguier, J.-L., & Burnet, F. (2005). Holes and entrainment in stratocumulus. Journal of the Atmospheric Sciences, 62, 443–459. https://doi.org/10.1175/JAS-3399.1 Gerber, H., Frick, G., Malinowski, S. P., Jonsson, H., Khelif, D., & Krueger, S. K. (2013). Entrainment rates and microphysics in POST stratocumulus. Journal of Geophysical Research, 118, 12094–12109. https://doi.org/10.1002/jgrd.50878 Gerber, H., Frick, G., Malinowski, S. P., Kumula, W., & Krueger, S. (2010). POST–A new look at stratocumulus. In 13th conference on cloud physics. Portland, OR: American Meteorological Society. Grabowski, W. W. (2014). Extracting microphysical impacts in large-eddy simulations of shallow convection. Journal of the Atmospheric Sciences, 71, 4493–4499. https://doi.org/10.1175/JAS-D-14-0231.1 Grabowski, W. W., & Smolarkiewicz, P. K. (1990). Monotone finite-difference approximations to the advection-condensation problem. Monthly Weather Review, 118, 2082–2098. https://doi.org/10.1175/1520-0493(1990)118<2082:MFDATT>2.0.CO;2 Grabowski, W. W., & Smolarkiewicz, P. K. (2002). A multiscale anelastic model for meteorological research. Monthly Weather Review, 130, 939–956. https://doi.org/10.1175/1520-0493(2002)130<0939:AMAMFM>2.0.CO;2 Grinstein, F. F., Margolin, L. G., & Rider, W. J. (2007). Implicit large eddy simulation: Computing turbulent fluid dynamics. New York, NY: Cambridge University Press. Guo, H., Liu, Y., Daum, P. H., Senum, G. I., & Tao, W.-K. (2008). Characteristics of vertical velocity in marine stratocumulus: Comparison of large eddy simulations with observations. Environmental Research Letters, 3, 045020. https://doi.org/10.1088/1748-9326/3/4/045020 Jarecka, D., Pawlowska, H., Grabowski, W. W., & Wyszogrodzki, A. A. (2013). Modeling microphysical effects of entrainment in clouds observed during EUCAARI-IMPACT field campaign. Atmospheric Chemistry and Physics, 13, 8489–8503. https://doi.org/10.5194/acp-13-8489-2013 Jen-La Plante, I., Ma, Y., Nurowska, K., Gerber, H., Khelif, D., Karpinska, K., et al. (2016). Physics of Stratocumulus Top (POST): Turbulence characteristics. Atmospheric Chemistry and Physics, 16, 9711–9725. https://doi.org/10.5194/acp-16-9711-2016 Kaimal, J. C., Wyngaard, J. C., Haugen, D. A., Coté, O. R., Izumi, Y., Caughey, S. J., et al. (1976). Turbulence structure in the convective boundary layer. Journal of the Atmospheric Sciences, 33, 2152–2169. https://doi.org/10.1175/1520-0469(1976)033<2152:TSITCB>2.0.CO;2 Katzwinkel, J., Siebert, H., & Shaw, R. A. (2012). Observation of a self-limiting, shear-induced turbulent inversion layer above marine stratocumulus. Boundary-Layer Meteorology, 145, 131–143. https://doi.org/10.1007/s10546-011-9683-4 Kazil, J., Yamaguchi, T., & Feingold, G. (2017). Mesoscale organization, entrainment, and the properties of a closed-cell stratocumulus cloud. Journal of Advances in Modeling Earth Systems, 9, 2214–2229. https://doi.org/10.1002/2017MS001072 Kelly, M., & Wyngaard, J. C. (2006). Two-dimensional spectra in the atmospheric boundary layer. Journal of the Atmospheric Sciences, 63, 3066–3070. https://doi.org/10.1175/JAS3769.1 Khairoutdinov, M. F., & Randall, D. A. (2003). Cloud resolving modeling of the ARM summer 1997 IOP: Model formulation, results, uncertainties, and sensitivities. Journal of the Atmospheric Sciences, 60, 607–625. https://doi.org/10.1175/1520-0469(2003)060<0607:CRMOTA>2.0.CO;2 Khani, S., & Waite, M. L. (2015). Large eddy simulations of stratified turbulence: The dynamic Smagorinsky model. Journal of Fluid Mechanics, 773, 327–344. https://doi.org/10.1017/jfm.2015.249 Kopec, M. K., Malinowski, S. P., & Piotrowski, Z. P. (2016). Effects of wind shear and radiative cooling on the stratocumulus-topped boundary layer. Quarterly Journal of the Royal Meteorological Society, 142, 3222–3233. https://doi.org/10.1002/qj.2903 Kurowski, M. J., Grabowski, W. W., & Smolarkiewicz, P. K. (2014). Anelastic and compressible simulation of moist deep convection. Journal of the Atmospheric Sciences, 71, 3767–3787. https://doi.org/10.1175/JAS-D-14-0017.1 Kurowski, M. J., Malinowski, S. P., & Grabowski, W. W. (2009). A numerical investigation of entrainment and transport within a stratocumulus-topped boundary layer. Quarterly Journal of the Royal Meteorological Society, 135, 77–92. https://doi.org/10.1002/qj.354 Lindborg, E. (2006). The energy cascade in a strongly stratified fluid. Journal of Fluid Mechanics, 550, 207–242. https://doi.org/10.1017/S0022112005008128 Malinowski, S. P., Gerber, H., Jen-La Plante, I., Kopec, M. K., Kumala, W., Nurowska, K., et al. (2013). Physics of Stratocumulus Top (POST): Turbulent mixing across capping inversion. Atmospheric Chemistry and Physics, 13, 12,171–12,186. https://doi.org/10.5194/acp-13-12171-2013 Margolin, L. G., & Rider, W. J. (2002). A rationale for implicit turbulence modelling. International Journal for Numerical Methods in Fluids, 39, 821–841. https://doi.org/10.1002/fld.331 Margolin, L. G., Rider, W. J., & Grinstein, F. F. (2006). Modeling turbulent flow with implicit LES. Journal of Turbulence, 7, N15. https://doi.org/10.1080/14685240500331595 Margolin, L. G., Smolarkiewicz, P. K., & Sorbjan, Z. (1999). Large-eddy simulations of convective boundary layers using nonoscillatory differencing. Physica D, 133, 390–397. https://doi.org/10.1016/S0167-2789(99)00083-4 Marstorp, L., Brethouwer, G., Grundestam, O., & Johansson, A. V. (2009). Explicit algebraic subgrid stress models with application to rotating channel flow. Journal of Fluid Mechanics, 639, 403–432. https://doi.org/10.1017/S0022112009991054 Matheou, G., & Chung, D. (2014). Large-eddy simulation of stratified turbulence. Part II: Application of the stretched-vortex model to the atmospheric boundary layer. Journal of the Atmospheric Sciences, 71, 4439–4460. https://doi.org/10.1175/JAS-D-13-0306.1 Mauritsen, T., & Svensson, G. (2007). Observations of stably stratified shear-driven atmospheric turbulence at low and high Richardson numbers. Journal of the Atmospheric Sciences, 64, 645–655. https://doi.org/10.1175/JAS3856.1 Mellado, J. P. (2010). The evaporatively driven cloud-top mixing layer. Journal of Fluid Mechanics, 660, 5–36. https://doi.org/10.1017/S0022112010002831 Mellado, J. P. (2017). Cloud-top entrainment in stratocumulus clouds. Annual Review of Fluid Mechanics, 49, 145–169. https://doi.org/10.1146/annurev-fluid-010816-060231 Mellado, J. P., Stevens, B., & Schmidt, H. (2014). Wind shear and buoyancy reversal at the top of stratocumulus. Journal of the Atmospheric Sciences, 71, 1040–1057. https://doi.org/10.1175/JAS-D-13-0189.1 Moeng, C.-H. (1986). Large-eddy simulation of a stratus-topped boundary layer. Part I: Structure and budgets. Journal of the Atmospheric Sciences, 43, 2886–2900. https://doi.org/10.1175/1520-0469(1986)043<2886:LESOAS>2.0.CO;2 Moeng, C.-H. (2000). Entrainment rate, cloud fraction, and liquid water path of PBL stratocumulus clouds. Journal of the Atmospheric Sciences, 57, 3627–3643. https://doi.org/10.1175/1520-0469(2000)057<3627:ERCFAL>2.0.CO;2 Montecchia, M., Brethouwer, G., Johansson, A. V., & Wallin, S. (2017). Taking large-eddy simulation of wall-bounded flows to higher Reynolds numbers by use of anisotropy-resolving subgrid models. Physical Review Fluids, 2, 034601. https://doi.org/10.1103/PhysRevFluids.2.034601 Morrison, H., & Grabowski, W. W. (2008). Modeling supersaturation and subgrid-scale mixing with two-moment bulk warm microphysics. Journal of the Atmospheric Sciences, 65, 792–812. https://doi.org/10.1175/2007JAS2374.1 Nishizawa, S., Yashiro, H., Sato, Y., Miyamoto, Y., & Tomita, H. (2015). Influence of grid aspect ratio on planetary boundary layer turbulence in large-eddy simulations. Geoscientific Model Development, 8, 3393–3419. https://doi.org/10.5194/gmd-8-3393-2015 Noda, A. T., & Satoh, M. (2014). Intermodel variances of subtropical stratocumulus environments simulated in CMIP5 models. Geophysical Research Letters, 41, 7754–7761. https://doi.org/10.1002/2014GL061812 Pedersen, J. G., Kelly, M., Gryning, S.-E., & Brümmer, B. (2013). The effect of unsteady and baroclinic forcing on predicted wind profiles in large eddy simulations: Two case studies of the daytime atmospheric boundary layer. Meteorologische Zeitschrift, 22, 661–674. https://doi.org/10.1127/0941-2948/2013/0477 Pedersen, J. G., Malinowski, S. P., & Grabowski, W. W. (2016). Resolution and domain-size sensitivity in implicit large-eddy simulation of the stratocumulus-topped boundary layer. Journal of Advances in Modeling Earth Systems, 8, 885–903. https://doi.org/10.1002/2015MS000572 Piotrowski, Z. P., Smolarkiewicz, P. K., Malinowski, S. P., & Wyszogrodzki, A. A. (2009). On numerical realizability of thermal convection. Journal of Computational Physics, 228, 6268–6290. https://doi.org/10.1016/j.jcp.2009.05.023 Pressel, K. G., Mishra, S., Schneider, T., Kaul, C. M., & Tan, Z. (2017). Numerics and subgrid-scale modeling in large eddy simulations of stratocumulus clouds. Journal of Advances in Modeling Earth Systems, 9, 1342–1365. https://doi.org/10.1002/2016MS000778 Prusa, J. M., Smolarkiewicz, P. K., & Wyszogrodzki, A. A. (2008). EULAG, A computational model for multiscale flows. Computers & Fluids, 37, 1193–1207. https://doi.org/10.1016/j.compfluid.2007.12.001 Riley, J. J., & Lelong, M.-P. (2000). Fluid motions in the presence of strong stable stratification. Annual Review of Fluid Mechanics, 32, 613–657. https://doi.org/10.1146/annurev.fluid.32.1.613 Schmidt, H., & Schumann, U. (1989). Coherent structure of the convective boundary layer derived from large-eddy simulations. Journal of Fluid Mechanics, 200, 511–562. https://doi.org/10.1017/S0022112089000753 Scotti, A., Meneveau, C., & Lilly, D. K. (1993). Generalized Smagorinsky model for anisotropic grids. Physics of Fluids A, 5, 2306–2308. https://doi.org/10.1063/1.858537 Smolarkiewicz, P. K. (2006). Multidimensional positive definite advection transport algorithm: An overview. International Journal for Numerical Methods in Fluids, 50, 1123–1144. https://doi.org/10.1002/fld.1071 Smyth, W. D., & Moum, J. N. (2000). Length scales of turbulence in stably stratified mixing layers. Physics of Fluids, 12, 1327–1342. https://doi.org/10.1063/1.870385 Sorbjan, Z. (1996). Numerical study of penetrative and “solid lid” nonpenetrative convective boundary layers. Journal of the Atmospheric Sciences, 53, 101–112. https://doi.org/10.1175/1520-0469(1996)053<0101:NSOPAL>2.0.CO;2 Stevens, B., Lenschow, D. H., Faloona, I., Moeng, C.-H., Lilly, D. K., Blomquist, B., et al. (2003b). On entrainment rates in nocturnal marine stratocumulus. Quarterly Journal of the Royal Meteorological Society, 129, 3469–3493. https://doi.org/10.1256/qj.02.202 Stevens, B., Lenschow, D. H., Vali, G., Gerber, H., Bandy, A., Blomquist, B., et al. (2003a). Dynamics and chemistry of marine stratocumulus—DYCOMS-II. Bulletin of the American Meteorological Society, 84, 579–593. https://doi.org/10.1175/BAMS-84-5-579 Stevens, B., Moeng, C.-H., Ackerman, A. S., Bretherton, C. S., Chlond, A., de Roode, S., et al. (2005). Evaluation of large-eddy simulations via observations of nocturnal marine stratocumulus. Monthly Weather Review, 133, 1443–1462. https://doi.org/10.1175/MWR2930.1 Sullivan, P. P., McWilliams, J. C., & Moeng, C.-H. (1994). A subgrid-scale model for large-eddy simulation of planetary boundary-layer flows. Boundary-Layer Meteorology, 71, 247–276. https://doi.org/10.1007/BF00713741 Sullivan, P. P., Weil, J. C., Patton, E. G., Jonker, H. J., & Mironov, D. V. (2016). Turbulent winds and temperature fronts in large-eddy simulations of the stable atmospheric boundary layer. Journal of the Atmospheric Sciences, 73, 1815–1840. https://doi.org/10.1175/JAS-D-15-0339.1 van der Dussen, J. J., de Roode, S. R., & Siebesma, A. P. (2014). Factors controlling rapid stratocumulus cloud thinning. Journal of the Atmospheric Sciences, 71, 655–664. https://doi.org/10.1175/JAS-D-13-0114.1 van der Dussen, J. J., de Roode, S. R., & Siebesma, A. P. (2016). How large-scale subsidence affects stratocumulus transitions. Atmospheric Chemistry and Physics, 16, 691–701. https://doi.org/10.5194/acp-16-691-2016 Waite, M. L. (2011). Stratified turbulence at the buoyancy scale. Physics of Fluids, 23, 066602. https://doi.org/10.1063/1.3599699 Wood, R. (2012). Stratocumulus clouds. Monthly Weather Review, 140, 2373–2423. https://doi.org/10.1175/MWR-D-11-00121.1 Wood, R., & Hartmann, D. L. (2006). Spatial variability of liquid water path in marine low cloud: The importance of mesoscale cellular convection. Journal of Climate, 19, 1748–1764. https://doi.org/10.1175/JCLI3702.1 Yamaguchi, T., Brewer, W. A., & Feingold, G. (2013). Evaluation of modeled stratocumulus-capped boundary layer turbulence with shipborne data. Journal of the Atmospheric Sciences, 70, 3895–3919. https://doi.org/10.1175/JAS-D-13-050.1 Yamaguchi, T., & Randall, D. A. (2012). Cooling of entrained parcels in a large-eddy simulation. Journal of the Atmospheric Sciences, 69, 1118–1136. https://doi.org/10.1175/JAS-D-11-080.1