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On the Convective-Scale Predictability of the Atmosphere On the Convective-Scale Predictability of the Atmosphere Lisa Bengtsson Cover image: Lightning in a convective cloud. (c) SMHI, reprinted with permission °c Lisa Bengtsson, Stockholm 2012 ISBN 978-91-7447-494-7 Printed by Universitetsservice US-AB, Stockholm, 2012 Distributor: Department of Meteorology Stockholm University Stockholm, Sweden Abstract A well-represented description of convection in weather and climate models is essential since convective clouds strongly influence the climate system. Con- vective processes interact with radiation, redistribute sensible and latent heat and momentum, and impact hydrological processes through precipitation. De- pending on the models’ horizontal resolution, the representation of convection may look very different. However, the convective scales not resolved by the model are traditionally parameterized by an ensemble of non-interacting con- vective plumes within some area of uniform forcing, representing the “large- scale”. A bulk representation of the mass-flux associated with the individual plumes in the defined area provides the statistical impact of moist convection on the atmosphere. Studying the characteristics of the ECMWF ensemble prediction system, it is found that the control forecast of the ensemble system is not variable enough in order to yield a sufficient spread using an initial perturbation technique alone. Such insufficient variability may be addressed in the parameterizations of, for instance, cumulus convection where the sub-grid variability in space and time is traditionally neglected. Furthermore, horizontal transport due to gravity waves can act to organize deep convection into larger-scale structures which can contribute to an up- scale energy cascade. However, horizontal advection and numerical diffusion are the only ways through which adjacent model grid-boxes interact in the models. The impact of flow dependent horizontal diffusion on resolved deep convection is studied, and the organization of convective clusters is found to be very sensitive to the method of imposing horizontal diffusion. However, using numerical diffusion in order to represent lateral effects is undesirable. To address the above issues, a scheme using cellular automata to introduce lateral communication, memory and a stochastic representation of the statis- tical effects of cumulus convection is implemented in two numerical weather models. The behaviour of the scheme is studied in cases of organized convec- tive squall-lines, and initial model runs show promising improvements. 3 List of Papers This thesis is based on the following papers, which are referred to in the text by their Roman numerals. I Bengtsson, L., Magnusson, L., Källén, E. (2008) Independent Estimations of the Asymptotic Variability in an Ensemble Fore- cast System Monthly Weather Review, Volume 136, Issue 11 pp. 4105-4112. (c)American Meteorological Society. Reprinted with permission. II Bengtsson, L., Tijm, S., Vána,ˇ F., Svensson, G. (2012) Impact of flow-dependent horizontal diffusion on resolved convection in AROME. Journal of Applied Meteorology and Climatology, Vol. 51, No.1, pp 54-67. (c)American Meteorological Society. Reprinted with permission. III Bengtsson, L., Körnich, H., Källén, E., Svensson, G. (2011) Large-Scale Dynamical Response to Subgrid-Scale Organization Provided by Cellular Automata. Journal of the Atmospheric Sciences Volume 68, Issue 12 pp. 3132-3144. (c)American Meteorological Society. Reprinted with permission. IV Bengtsson, L., Steinheimer, M., Bechtold, P., Geleyn, J-F. (2012) A stochastic parameterization for deep convection using cellu- lar automata. Submitted to Journal of the Atmospheric Sciences, February 2012. Reprints were made with permission from the American Meteorological Soci- ety. The idea behind Paper I was initiated by Erland Källén. Originally the pa- per focused on the relation between ensemble mean and the individual mem- bers at infinite forecast length. Linus Magnusson added a contribution on how the two relate to ensemble spread. I did all the analysis and wrote the text. The idea behind Paper II was my own, spawning from of sensitivity stud- ies made together with Sander Tijm. I performed most of the analysis, with contributions from Sander Tijm, and wrote most of the text with invaluable insight from Filip Vána,ˇ and smaller contributions from Gunilla Svensson. The idea behind Paper III was initiated by Erland Källén. I did all of the code developments, analysis and wrote most of the text following invaluable sci- entific discussion together with Heiner Körnich, Erland Källén and Gunilla Svensson. The general idea behind Paper IV was my own, as a natural exten- 5 sion of Paper III in line with my work at SMHI. The implementation ideas in the ALARO model were developed in close collaboration with Jean-François Geleyn. The model code describing the cellular automata in IFS was intro- duced by Martin Steinheimer. Modifications to the code to perform limited area simulations with deterministic rules were done by myself. I did all of the code developments and analysis in regards to the ALARO simulations. The ECMWF implementation ideas, probabilistic rules, and option to run the cel- lular automata using sub-grid advection are credited to Martin Steinheimer. The ECMWF model runs and analysis in Paper IV was performed by Peter Bechtold. 6 Contents 1 Numerical weather prediction ................................. 9 1.1 Representing model uncertainty: ensemble prediction ..................... 10 1.2 Asymptotic error growth: results from Paper I .......................... 12 2 Weather prediction at differing atmospheric scales ................... 15 2.1 Equatorial wave modes ......................................... 17 3 Uncertainty due to parameterization of cumulus convection ............ 21 3.1 Parameterization of cumulus convection .............................. 23 3.1.1 Cloud model ............................................ 23 3.1.2 Closure ............................................... 26 3.2 Lateral communication and convective organization: results from Papers II, III and IV 29 3.3 Stochastic representation of cumulus convection; results from Papers III and IV .... 32 4 Future Outlook ............................................ 33 5 Acknowledgements ........................................ 35 Bibliography ................................................ 37 1. Numerical weather prediction Numerical Weather Prediction (NWP) models are the main tools used in or- der to make weather forecasts. In NWP, the state of the atmosphere at some future time is determined using the primitive equations of fluid dynamics and thermodynamics based on an analysis of the current conditions. The very first operational, real-time +72 h NWP in the world was run in Sweden in autumn 1954 for the Swedish Armed Forces by the Department of Meteorology at Stockholm University, and operational production started shortly thereafter (Persson, 2005). The primitive equations consist of conservation of momentum, mass- conservation of dry air, the ideal gas law, the first law of thermodynamics and the thermodynamic equation for conservation of water. Following the notation of Kalnay (2003), the momentum equation and continuity equation used to describe the system are: dV = α∇p 2Ω V gk + F (1.1) dt − − × − b ∂ρ = ∇ (ρV) (1.2) ∂t − · where V is the three-dimensional velocity vector, F is the frictional force, p is pressure, ρ is density and α is its inverse. The thermodynamic equations for heat and moisture are: dT dp Q = Cp α (1.3) dt − dt ∂ρq = ∇ (ρVq)+ ρ(e c) (1.4) dt − · − where Q is the diabatic heating or cooling, T is temperature and Cp is the specific heat at constant pressure. q is the specific humidity and e and c are the condensation and evaporation rates. Finally the ideal gas-law is: pα = RT (1.5) where R is the gas constant. Equations 1.1 to 1.4 are non-linear partial differential equations which are impossible to solve exactly through analytical methods. Therefore, the equa- tions are solved using numerical methods by discretization either in spatial or 9 spectral space, to yield an approximate solution. Processes contributing to the evolution of the primitive equations which are not resolved in space or time on the numerical grid need to be represented by a parameterization. Following Bjerknes (1904) weather forecasting should be considered as an initial value problem of mathematical physics, and could be carried out by integrating the Eqns. 1.1 to 1.5 forward in time, starting from the observed, initial state of the atmosphere. In order to construct an initial condition to numerically solve the primitive equations, an analysis of the present state of the atmosphere is constructed using observations of the current conditions combined with the forecast from the previous forecast cycle. Most NWP models today use observations from meteorological observation sites, airports, ships, buoys, airplanes and radiosondes, as well as remote sens- ing such as satellite and radar (Gustafsson et al., 2012). For high-resolution limited area models, radar observations and ground-based GPS observations can be used in order to describe the initial state with increasing accuracy. Due to the spatial and temporal irregularities in observations of the current state of the atmosphere, the information provided by observations are combined with a background field from the previous forecast cycle in order to assimilate the initial state on the uniform NWP grid. The technique to do so varies among different NWP models; examples
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