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Effects of terrain-following vertical coordinates on simulation of stratus clouds in numerical weather prediction models
Corresponding Author
Stephanie Westerhuis
ETH Zurich, Switzerland
Federal Institute of Meteorology and Climatology (MeteoSwiss), Zürich, Switzerland
Correspondence
S. Westerhuis, MeteoSwiss, Zürich CH-8058, Switzerland.
Email: [email protected]
Search for more papers by this authorOliver Fuhrer
Federal Institute of Meteorology and Climatology (MeteoSwiss), Zürich, Switzerland
Vulcan Inc., Seattle, Washington, USA
Search for more papers by this authorRitthik Bhattacharya
Goethe University of Frankfurt, Frankfurt am Main, Germany
Search for more papers by this authorJürg Schmidli
Goethe University of Frankfurt, Frankfurt am Main, Germany
Search for more papers by this authorChristopher Bretherton
Vulcan Inc., Seattle, Washington, USA
Department of Atmospheric Sciences, University of Washington, Seattle, WA, USA
Search for more papers by this authorCorresponding Author
Stephanie Westerhuis
ETH Zurich, Switzerland
Federal Institute of Meteorology and Climatology (MeteoSwiss), Zürich, Switzerland
Correspondence
S. Westerhuis, MeteoSwiss, Zürich CH-8058, Switzerland.
Email: [email protected]
Search for more papers by this authorOliver Fuhrer
Federal Institute of Meteorology and Climatology (MeteoSwiss), Zürich, Switzerland
Vulcan Inc., Seattle, Washington, USA
Search for more papers by this authorRitthik Bhattacharya
Goethe University of Frankfurt, Frankfurt am Main, Germany
Search for more papers by this authorJürg Schmidli
Goethe University of Frankfurt, Frankfurt am Main, Germany
Search for more papers by this authorChristopher Bretherton
Vulcan Inc., Seattle, Washington, USA
Department of Atmospheric Sciences, University of Washington, Seattle, WA, USA
Search for more papers by this authorFunding information: ETH research grant MeteoSwiss the Hans Ertel Centre of DWD, Grant/Award Numbers: ETH-17 16-2;123001738;4818DWDP4
Abstract
Many numerical weather prediction models employ terrain-following vertical coordinates. As a consequence, over orography, flat tops of stratus clouds are intersected by the vertical coordinate surfaces. We conduct idealised two-dimensional simulations of a stratus cloud with the COSMO model to study the effect of such sloping vertical coordinate surfaces. The evolution of the stratus cloud above a flat surface within a horizontally homogeneous atmosphere serves as a reference. During night-time, the cloud thickens, driven by radiative cooling at the cloud top. Adding a sinusoidal perturbation to the vertical coordinate surfaces reduces the growth of the stratus cloud. With strong perturbations, the cloud starts to dissipate. The physical processes in the two simulations are identical, hence this behaviour is purely driven by numerical diffusion. The cloud is similarly thinned when sinusoidal orographic features are introduced. The reduction depends on the amplitude and wavelength of the perturbations and hills. Increasing the horizontal resolution partly mitigates the numerical diffusion. However, this is a very costly measure for an operational weather model. We suggest conducting further research on a new vertical coordinate with additional local smoothing of the orographic signal.
REFERENCES
- Adcroft, A., Hill, C. and Marshall, J. (1997) Representation of topography by shaved cells in a height coordinate ocean model. Monthly Weather Review, 125(9), 2293–2315.
- Arakawa, A. and Lamb, V.R. (1977) Computational design of the basic dynamical processes of the UCLA general circulation model. Methods in Computational Physics: Advances in Research and Applications, 17, 173–265. https://doi.org/10.1016/B978-0-12-460817-7.50009-4.
10.1016/B978‐0‐12‐460817‐7.50009‐4 Google Scholar
- Baba, Y. and Takahashi, K. (2013) Weighted essentially non-oscillatory scheme for cloud edge problem. Quarterly Journal of the Royal Meteorological Society, 139, 1374–1388.
- Baldauf, M., Seifert, A., Förstner, J., Majewski, D., Raschendorfer, M. and Reinhardt, T. (2011) Operational convective-scale numerical weather prediction with the COSMO model: Description and sensitivities. Monthly Weather Review, 139(12), 3887–3905.
- Bergot, T. (2016) Large-eddy simulation study of the dissipation of radiation fog. Quarterly Journal of the Royal Meteorological Society, 142, 1029–1040.
- Bierdel, L., Friederichs, P. and Bentzien, S. (2012) Spatial kinetic energy spectra in the convection-permitting limited-area NWP model COSMO-DE. Meteorologische Zeitschrift, 21(3), 245–258.
- Bott, A. (1989) A positive definite advection scheme obtained by nonlinear renormalization of the advective fluxes. Monthly Weather Review, 117(5), 1006–1016.
- Buzzi, M. (2008) Challenges in operational numerical weather prediction at high resolution in complex terrain. PhD thesis, ETH Zürich, Switzerland.
- Doms, G. and Baldauf, M. (2011). A description of the nonhydrostatic regional model LM, Part I: Dynamics and numerics. COSMO documentation, DWD, Offenbach, Germany.
- Förstner, J. and Doms, G. (2004) Runge–Kutta time integration and high-order spatial discretization of advection – a new dynamical core for the LMK. COSMO Newsletter, 4, 168–176.
- Gal-Chen, T. and Somerville, R.C. (1975) Numerical solution of the Navier–Stokes equations with topography. Journal of Computational Physics, 17(3), 276–310.
- Haney, R.L. (1991) On the pressure gradient force over steep topography in sigma-coordinate ocean models. Journal of Physical Oceanography, 21(4), 610–619.
- Heise, E., Ritter, B. and Schrodin, R. (2006). Operational implementation of the multilayer soil model. COSMO Technical Report 9, DWD, Offenbach, Germany.
- Kasahara, A. (1974) Various vertical coordinate systems used for numerical weather prediction. Monthly Weather Review, 102(7), 509–522.
- Kirkpatrick, M., Armfield, S. and Kent, J. (2003) A representation of curved boundaries for the solution of the Navier–Stokes equations on a staggered three-dimensional Cartesian grid. Journal of Computational Physics, 184(1), 1–36.
- Klemp, J.B., Skamarock, W.C. and Fuhrer, O. (2003) Numerical consistency of metric terms in terrain-following coordinates. Monthly Weather Review, 131(7), 1229–1239.
- Klemp, J.B. and Wilhelmson, R.B. (1978) The simulation of three-dimensional convective storm dynamics. Journal of the Atmospheric Sciences, 35(6), 1070–1096.
- Langhans, W., Fuhrer, O. and Schmidli, J. (2012) Description and application of a budget-diagnosis tool in COSMO. COSMO Newsletter, 12, 43–51.
- Leuenberger, D., Koller, M., Fuhrer, O. and Schär, C. (2010) A generalization of the SLEVE vertical coordinate. Monthly Weather Review, 138(9), 3683–3689.
- Lohmann, U., Lüönd, F. and Mahrt, F. (2016) An Introduction to Clouds: from the microscale to climate. Cambridge University Press, Cambridge, UK.
10.1017/CBO9781139087513 Google Scholar
- Lundquist, K.A., Chow, F.K. and Lundquist, J.K. (2012) An immersed boundary method enabling large-eddy simulations of flow over complex terrain in the WRF model. Monthly Weather Review, 140(12), 3936–3955.
- Lunet, T., Lac, C., Auguste, F., Visentin, F., Masson, V. and Escobar, J. (2017) Combination of WENO and explicit Runge–Kutta methods for wind transport in the Meso-NH model. Monthly Weather Review, 145(9), 3817–3838.
- Mellor, G.L. and Yamada, T. (1974) A hierarchy of turbulence closure models for planetary boundary layers. Journal of the Atmospheric Sciences, 31(7), 1791–1806.
- Mellor, G.L. and Yamada, T. (1982) Development of a turbulence closure model for geophysical fluid problems. Reviews of Geophysics, 20(4), 851–875.
- Mesinger, F. and Janjić, Z.I. (1985) Problems and numerical methods of the incorporation of mountains in atmospheric models. Lectures in Applied Mathematics, 22, 81–120.
- Mesinger, F., Janjić, Z.I., Ničković, S., Gavrilov, D. and Deaven, D.G. (1988) The step-mountain coordinate: Model description and performance for cases of Alpine lee cyclogenesis and for a case of an Appalachian redevelopment. Monthly Weather Review, 116(7), 1493–1518.
- Ogaja, J. and Will, A. (2016) Fourth-order conservative discretization of horizontal Euler equations in the COSMO model and regional climate simulations. Meteorologische Zeitschrift, 10, 577–605.
- Raschendorfer, M. (2001) The new turbulence parameterization of LM. COSMO Newsletter, 1, 89–97.
- Raymond, W.H. (1988) High-order low-pass implicit tangent filters for use in finite-area calculations. Monthly Weather Review, 116(11), 2132–2141.
- Reinhardt, T. and Seifert, A. (2006) A three-category ice scheme for the LMK. COSMO Newsletter, 6, 115–120.
- Ricard, D., Lac, C., Riette, S., Legrand, R. and Mary, A. (2013) Kinetic energy spectra characteristics of two convection-permitting limited-area models AROME and Meso-NH. Quarterly Journal of the Royal Meteorological Society, 139, 1327–1341.
- Ritter, B. and Geleyn, J.-F. (1992) A comprehensive radiation scheme for numerical weather prediction models with potential applications in climate simulations. Monthly Weather Review, 120(2), 303–325.
- Schär, C., Leuenberger, D., Fuhrer, O., Lüthi, D. and Girard, C. (2002) A new terrain-following vertical coordinate formulation for atmospheric prediction models. Monthly Weather Review, 130(10), 2459–2480.
- Schmidli, J., Böing, S. and Fuhrer, O. (2018) Accuracy of simulated diurnal valley winds in the Swiss Alps: Influence of grid resolution, topography filtering, and land surface datasets. Atmosphere, 9(5), 196
- Schneider, W. and Bott, A. (2014) On the time-splitting errors of one-dimensional advection schemes in numerical weather prediction models; a comparative study. Quarterly Journal of the Royal Meteorological Society, 140, 2321–2329.
- Skamarock, W.C. (2004) Evaluating mesoscale NWP models using kinetic energy spectra. Monthly Weather Review, 132(12), 3019–3032.
- Steppeler, J., Doms, G., Schättler, U., Bitzer, H., Gassmann, A., Damrath, U. and Gregoric, G. (2003) Meso-gamma scale forecasts using the nonhydrostatic model LM. Meteorology and Atmospheric Physics, 82(1–4), 75–96.
- Strang, G. (1968) On the construction and comparison of difference schemes. SIAM Journal on Numerical Analysis, 5(3), 506–517.
- Tseng, Y.-H. and Ferziger, J.H. (2003) A ghost-cell immersed boundary method for flow in complex geometry. Journal of Computational Physics, 192(2), 593–623.
- Tudor, M. (2010) Impact of horizontal diffusion, radiation and cloudiness parameterization schemes on fog forecasting in valleys. Meteorology and Atmospheric Physics, 108(1–2), 57–70.
- Westerhuis, S., Fuhrer, O., Cermak, J. and Eugster, W. (2020) Identifying the key challenges for fog and low stratus forecasting in complex terrain. Quarterly Journal of the Royal Meteorological Society. https://doi.org/10.1002/qj.3849.
- Weusthoff, T., Ament, F., Arpagaus, M. and Rotach, M.W. (2010) Assessing the benefits of convection-permitting models by neighborhood verification: Examples from MAP D-PHASE. Monthly Weather Review, 138(9), 3418–3433.
- Wicker, L.J. and Skamarock, W.C. (2002) Time-splitting methods for elastic models using forward time schemes. Monthly Weather Review, 130(8), 2088–2097.
- Wilson, T.H. and Fovell, R.G. (2018) Modeling the evolution and life cycle of radiative cold pools and fog. Weather and Forecasting, 33(1), 203–220.
- Zängl, G. (2002) An improved method for computing horizontal diffusion in a sigma-coordinate model and its application to simulations over mountainous topography. Monthly Weather Review, 130(5), 1423–1432.
- Zängl, G. (2012) Extending the numerical stability limit of terrain-following coordinate models over steep slopes. Monthly Weather Review, 140(11), 3722–3733.
- Zhu, Z., Thuburn, J., Hoskins, B.J. and Haynes, P.H. (1992) A vertical finite-difference scheme based on a hybrid
-
-p coordinate. Monthly Weather Review, 120(5), 851–862.