Algorithm Theoretical Definition Document (ATDD) for product. PR-ASS-1 - Instantaneous and accumulated precipitation at ground computed by a NWP model

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1 Algorithms Theoretical Definition Document, 31 August ATDD-06 (Product PR-ASS-1) Page 1 Italian Meteorological Service Italian Department of Civil Defence Algorithm Theoretical Definition Document (ATDD) for product PR-ASS-1 - Instantaneous and accumulated precipitation at ground computed by a NWP model Zentralanstalt für Meteorologie und Geodynamik Vienna University of Technology Institut für Photogrammetrie und Fernerkundung Royal Meteorological Institute of Belgium European Centre for Medium-Range Weather Forecasts Finnish Meteorological Institute Finnish Environment Institute Helsinki University of Technology Météo-France CNRS Laboratoire Atmosphères, Milieux, Observations Spatiales CNRS Centre d'etudes Spatiales de la BIOsphere Bundesanstalt für Gewässerkunde Hungarian Meteorological Service CNR - Istituto Scienze dell Atmosfera e del Clima Università di Ferrara Institute of Meteorology and Water Management Romania National Meteorological Administration Slovak Hydro-Meteorological Institute Turkish State Meteorological Service Middle East Technical University Istanbul Technical University Anadolu University 31 August 2010

2 Algorithms Theoretical Definition Document, 31 August ATDD-06 (Product PR-ASS-1) Page 2 Algorithm Theoretical Definition Document ATDD-06 Product PR-ASS-1 Instantaneous and accumulated precipitation at ground computed by a NWP model INDEX Page Acronyms The EUMETSAT Satellite Application Facilities and H-SAF Introduction to product PR-ASS Principle of the product Main operational characteristics Architecture of the products generation chain Product development team Short description of the COSMO-ME model Algorithms description Quantitative Precipitation Forecast The cloud-precipitation module Algorithm validation/heritage Examples of PR-ASS-1 products 15 References 16 List of Tables Table 01 List of H-SAF products 05 Table 02 Development team for product PR-ASS-1 07 Table 03 COSMO model formulation: dynamics and numerics 09 Table 04 COSMO model formulation: physical parameterizations 10 List of Figures Fig. 01 Conceptual scheme of the EUMETSAT application ground segment 05 Fig. 02 Current composition of the EUMETSAT SAF network (in order of establishment) 05 Fig. 03 Products generation chain for PR-ASS-1 07 Fig. 04 Current coverage of COSMO-ME 11 Fig. 05 Envisaged coverage for product PR-ASS-1 11 Fig. 06 Cloud microphysical processes considered in the two-category ice scheme 13 Fig hour accumulated precipitation from COSMO-ME for 5 Feb 2008, 00 UTC. 15 Forecast run initialised at 00 UTC of 4 Feb 2008 Fig. 08 Instantaneous precipitation from COSMO-ME for 5 Feb 2008, 00 UTC. Forecast run initialised at 00 UTC of 4 Feb

3 Algorithms Theoretical Definition Document, 31 August ATDD-06 (Product PR-ASS-1) Page 3 Acronyms ATDD Algorithms Theoretical Definition Document AU Anadolu University (in Turkey) BfG Bundesanstalt für Gewässerkunde (in Germany) CAF Central Application Facility (of EUMETSAT) CAPE Convective Available Potential Energy CDOP Continuous Development-Operation Phase CESBIO Centre d'etudes Spatiales de la BIOsphere (of CNRS, in France) CM-SAF SAF on Climate Monitoring CNMCA Centro Nazionale di Meteorologia e Climatologia Aeronautica (in Italy) CNR Consiglio Nazionale delle Ricerche (of Italy) CNRS Centre Nationale de la Recherche Scientifique (of France) COSMO Consortium for Small-Scale Modelling COSMO-ME Consortium for Small-Scale Modelling - version for Mediterranean DPC Dipartimento Protezione Civile (of Italy) EARS EUMETSAT Advanced Retransmission Service ECMWF European Centre for Medium-range Weather Forecasts EDC EUMETSAT Data Centre, previously known as U-MARF EUM Short for EUMETSAT EUMETCast EUMETSAT s Broadcast System for Environmental Data EUMETSAT European Organisation for the Exploitation of Meteorological Satellites FMI Finnish Meteorological Institute FTP File Transfer Protocol GEO Geostationary Earth Orbit GRAS-SAF SAF on GRAS Meteorology H-SAF SAF on Support to Operational Hydrology and Water Management IMWM Institute of Meteorology and Water Management (in Poland) IPF Institut für Photogrammetrie und Fernerkundung (of TU-Wien, in Austria) IR Infra Red IRM Institut Royal Météorologique (of Belgium) (alternative of RMI) ISAC Istituto di Scienze dell Atmosfera e del Clima (of CNR, Italy) ITU İstanbul Technical University (in Turkey) LATMOS Laboratoire Atmosphères, Milieux, Observations Spatiales (of CNRS, in France) LEO Low Earth Orbit LSA-SAF SAF on Land Surface Analysis Météo France National Meteorological Service of France METU Middle East Technical University (in Turkey) MW Micro Wave NMA National Meteorological Administration (of Romania) NOAA National Oceanic and Atmospheric Administration (Agency and satellite) NWC-SAF SAF in support to Nowcasting & Very Short Range Forecasting NWP Numerical Weather Prediction NWP-SAF SAF on Numerical Weather Prediction O3M-SAF SAF on Ozone and Atmospheric Chemistry Monitoring OMSZ Hungarian Meteorological Service OSI-SAF SAF on Ocean and Sea Ice PP Project Plan PUM Product User Manual PVR Product Validation Report QPF Quantitative Precipitation Forecast RMI Royal Meteorological Institute (of Belgium) (alternative of IRM) SAF Satellite Application Facility

4 Algorithms Theoretical Definition Document, 31 August ATDD-06 (Product PR-ASS-1) Page 4 SHMÚ SYKE TKK TSMS TU-Wien U-MARF UniFe URD UTC VIS ZAMG Slovak Hydro-Meteorological Institute Suomen ympäristökeskus (Finnish Environment Institute) Teknillinen korkeakoulu (Helsinki University of Technology) Turkish State Meteorological Service Technische Universität Wien (in Austria) Unified Meteorological Archive and Retrieval Facility University of Ferrara (in Italy) User Requirements Document Universal Coordinated Time Visible Zentralanstalt für Meteorologie und Geodynamik (of Austria)

5 Algorithms Theoretical Definition Document, 31 August ATDD-06 (Product PR-ASS-1) Page 5 1. The EUMETSAT Satellite Application Facilities and H-SAF The EUMETSAT Satellite Application Facility on Support to Operational Hydrology and Water Management (H-SAF) is part of the distributed application ground segment of the European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT). The application ground segment consists of a Central Application Facility (CAF) and a network of eight Satellite Application Facilities (SAFs) dedicated to development and operational activities to provide satellitederived data to support specific user communities. See Fig. 01. EUM Geostationary Systems Data Acquisition and Control Data Processing EUMETSAT HQ Systems of the EUM/NOAA Cooperation other data sources Application Ground Segment Meteorological Products Extraction EUMETSAT HQ Archive & Retrieval Facility (Data Centre) EUMETSAT HQ Satellite Application Facilities (SAFs) Centralised processing and generation of products Decentralised processing and generation of products USERS Fig Conceptual scheme of the EUMETSAT application ground segment. Fig. 02 reminds the current composition of the EUMETSAT SAF network (in order of establishment). Nowcasting & Very Short Range Forecasting Ocean and Sea Ice Ozone & Atmospheric Numerical Weather Climate Monitoring Chemistry Monitoring Prediction GRAS Meteorology Land Surface Analysis Operational Hydrology & Water Management Fig Current composition of the EUMETSAT SAF network (in order of establishment). The H-SAF was established by the EUMETSAT Council on 3 July 2005; its Development Phase started on 1 st September 2005 and ends on 31 August The list of H-SAF products is shown in Table 01. Table 01 - List of H-SAF products Code Acronym Product name H01 PR-OBS-1 Precipitation rate at ground by MW conical scanners (with indication of phase) H02 PR-OBS-2 Precipitation rate at ground by MW cross-track scanners (with indication of phase) H03 PR-OBS-3 Precipitation rate at ground by GEO/IR supported by LEO/MW H04 PR-OBS-4 Precipitation rate at ground by LEO/MW supported by GEO/IR (with flag for phase) H05 PR-OBS-5 Accumulated precipitation at ground by blended MW and IR H06 PR-ASS-1 Instantaneous and accumulated precipitation at ground computed by a NWP model H07 SM-OBS-1 Large-scale surface soil moisture by radar scatterometer H08 SM-OBS-2 Small-scale surface soil moisture by radar scatterometer H09 SM-ASS-1 Volumetric soil moisture (roots region) by scatterometer assimilation in NWP model H10 SN-OBS-1 Snow detection (snow mask) by VIS/IR radiometry H11 SN-OBS-2 Snow status (dry/wet) by MW radiometry H12 SN-OBS-3 Effective snow cover by VIS/IR radiometry H13 SN-OBS-4 Snow water equivalent by MW radiometry

6 Algorithms Theoretical Definition Document, 31 August ATDD-06 (Product PR-ASS-1) Page 6 2. Introduction to product PR-ASS Principle of the product Product PR-ASS-1 (Instantaneous and accumulated precipitation at ground computed by a NWP model) is the output of the operational COSMO-ME NWP model in use at CNMCA. The role of PR- ASS-1 is to provide a background precipitation field regular in space and time, unlike satellite-derived observations that are available at changing times and locations, depending on the specific orbit. The product has been developed, is operationally running and is being progressively improved at CNMCA. It is a best effort product, not charged on the H-SAF budget. To be accepted with the limitations (and the advantages) of being integrated in a fully operational environment continuously being monitored, updated and improved at intervals. The main limitations are the covered area and the number of runs/day, that will not meet H-SAF requirement by the end of the Development Phase but will be progressively mitigated during the Continuous Development-Operation Phase (CDOP). For more information, please refer to the Products User Manual (specifically, PUM-06), 2.2 Main operational characteristics The operational characteristics of PR-ASS-1 are discussed in PUM-06. Here are the main highlights. The horizontal resolution ( x), for a product generated by a NWP model, depends on the scale of motion correctly represented in the model. For COSMO-ME, as concerns precipitation products, it is estimated as ~ 30 km. The sampling interval consist of the model grid mesh ~ 7 km. Thus: resolution x ~ 30 km - sampling distance: 7 km. The observing cycle ( t). All products are outputted at 3-hour intervals. This is the sampling interval for the product. However, they derive from forecasting cycles that currently are run at 00 and 12 UTC, therefore the output products are correlated. It is correct to quote an observing cycle ~ 12 h (to be reduced to t ~ 6 h in the near future, when runs at 06 and 18 UTC will be added). Thus: observing cycle t ~ 12 h - sampling time: 3 h. The timeliness (δ), for a product from a NWP process, is intended as the difference between the nominal time of the run start and the availability of forecast products, inclusive of the window cut-off for observation collection, analysis, initialisation, processing and output stabilisation. For COSMO-ME we currently have: timeliness δ ~ 4 h. The accuracy stems from the overall model performance, and the specific performance of the cloudprecipitation representation. It is evaluated a-posteriori by means of the validation activity. See Product Validation Report PVR Architecture of the products generation chain The architecture of the PR-ASS-1 product generation chain is shown in Fig. 03

7 Algorithms Theoretical Definition Document, 31 August ATDD-06 (Product PR-ASS-1) Page 7 Satellite observations Assimilation & initialisation Ground-based observations High resolution model Integration Precipitation rate PR-ASS-1 Accumulated precipitation End-users and H-SAF central archive Fig Products generation chain for PR-ASS-1. The output consists of five figures at 3-hour intervals: the precipitation rate and the accumulated precipitation over the previous 3, 6, 12 and 24 hours. The product is disseminated to the Users by FTP and also intended to be utilised internally in support of other H-SAF products, especially PR-OBS-5 (Accumulated precipitation at ground by blended MW and IR), for constraining the output in order to reduce biases [not yet implemented]. 2.4 Product development team Names and coordinates of the main actors for PR-ASS-1 algorithm development and integration are listed in Table 02. Lucio Torrisi (Leader) Francesca Marcucci David Palella Table 02 - Development team for product PR-ASS-1 Centro Nazionale di Meteorologia e Climatologia Aeronautica (CNMCA) Italy l.torrisi@meteoam.it marcucci@meteoam.it palella@meteoam.it

8 Algorithms Theoretical Definition Document, 31 August ATDD-06 (Product PR-ASS-1) Page 8 3. Short description of the COSMO-ME model COSMO-ME is the CNMCA (Centro Nazionale di Meteorologia e Climatologia Aeronautica of the Italian Meteorological Service) operational set-up of the non-hydrostatic regional model developed by the Consortium for Small-Scale Modelling (COSMO: The regional model COSMO is based on the primitive hydro-thermodynamical equations describing compressible non-hydrostatic flow in a moist atmosphere without any scale approximations. A basic state is subtracted from the equations to reduce numerical errors associated with the calculation of the pressure gradient force in case of sloping coordinate surfaces. The basic state represents a timeindependent dry atmosphere at rest which is prescribed to be horizontally homogeneous, vertically stratified and in hydrostatic balance. In an atmospheric model the dynamics typically is the equation set (basic equations) without the forcing terms due to the parametrized subgrid physical processes (physics). The basic equations are written in advection form and the continuity equation is replaced by a prognostic equation for the perturbation pressure (i.e. the deviation of pressure from the reference state). The model equations are solved numerically using the traditional finite difference method. Table 03 summarizes the dynamical and numerical key features of the COSMO model.

9 Algorithms Theoretical Definition Document, 31 August ATDD-06 (Product PR-ASS-1) Page 9 Table 03 - COSMO model formulation: dynamics and numerics Model Equations Basic hydro-thermodynamical equations in advection form, No scale approximations (i.e. fully compressible and non-hydrostatic), Substraction of horizontally homogeneous basic state at rest. Prognostic Variables Horizontal and vertical wind components (u, v, w), Temperature (T), Pressure perturbation (p', deviation from the reference state), Specific humidity (qv), Specific cloud water content (qc) Specific cloud ice content (qi) Specific rain content (qr) Specific snow content (qs) Turbulent kinetic energy (tke) Optionally, specific graupel content (qg) Coordinate System Rotated geographical (lat/lon) coordinate system horizontally, Generalized terrain-following height-coordinate vertically. Grid Structure Arakawa C-grid, Lorenz vertical grid staggering Spatial Discretization Second-order horizontal and vertical differencing (centred) Time Integration Time-level (Leapfrog) split explicit using extensions proposed by Skamarock and Klemp (1992). Additional Options: - 2 time-level Runge-Kutta 3rd-order scheme (regular or TVD) with various options for high-order spatial discretization (Forstner and Doms, 2004), - time-level semi-implicit scheme (Thomas et al., 2000), - 2 time-level Runge-Kutta 2nd order split-explicit scheme (Wicker and Skamarock, 1998). Numerical Smoothing Rayleigh damping layer at upper boundary 4th order linear horizontal diffusion with option for a monotonic version including an orographic limiter, 3-D divergence damping and off-centering in split steps Lateral Boundaries 1-way nesting using the lateral boundary formulation to Davies and Turner (1977). Initialization Diabatic digital filtering initialization scheme (Lynch et al. 1997) A variety of subgrid-scale physical processes are taken into account by parameterization schemes. Table 04 gives a short overview on the parameterization schemes used operationally and on additional options implemented so far.

10 Algorithms Theoretical Definition Document, 31 August ATDD-06 (Product PR-ASS-1) Page 10 Table 04 - COSMO model formulation: physical parameterizations Grid-Scale Clouds and Precipitation Cloud water formation dissipation by saturation adjustment. Precipitation formation by a bulk-parameterization including water vapour, cloud water, cloud ice, rain and snow as hydrometeor categories (Doms 2002; Baldauf and Schultz 2004; Reinhardt and Seifert 2006). Subgrid-Scale Clouds Subgrid-scale cloudiness (fractional cloud cover) is interpreted by an empirical function depending on relative humidity. A corresponding cloud water content is also diagnosed. Moist Convection Mass-flux convection scheme after Tiedtke (1989) with closure based on moisture convergence. Option for a modified closure based on CAPE. Radiation δ-two stream radiation scheme based on Ritter and Geylen (1989) for short- and longwave fluxes; full cloud-radiation feedback. Turbulent Diffusion Level 2.5-scheme with a prognostic treatment of turbulent kinetic energy; effects of subgrid-scale condensation and evaporation are included. Optionally, diagnostic K-closure (at hierarchy level 2) for vertical diffusion. Subgrid-scale orography Blocked flow and gravity wave drag (Lott and Miller, 1997). Surface Layer Scheme based on turbulent kinetic energy; includes effects from subgrid-scale thermal circulations. Optionally, constant flux layer parameterization. Soil Processes Multi-layer soil model including freezing of soil water (Schrodin and Heise, 2001). Optionally, two-layer soil model after Jacobsen and Heise (1984) with Penman-Monteith type transpiration. Snow and interception storage are included. Climate values changing monthly (but fixed during forecast) in third layer. The COSMO-ME domain covers most of Europe and has a 7 km horizontal grid spacing and 40 vertical levels with a top at about 22 km. COSMO-ME integration is driven by IFS boundary conditions and initialised by analysis fields from the CNMCA variational data assimilation system. Some adaptation to COSMO-ME setup have to be performed to comply with H-SAF requirements: enlargement of the integration domain; elevation of the top model layer. The enlargement of the COSMO-ME area (see Fig. 04 for visualising the current coverage) is needed to geographically cover all the participating countries (see Fig. 05). It will involve the following steps: change the pole of the rotated lat-lon grid to optimise the domain coverage; retrieval and quality control of physiographic parameters (soil type, vegetation parameters, etc.); reconfiguration of boundary conditions files; reconfiguration of operational scripts; test of the new operational configuration.

11 Algorithms Theoretical Definition Document, 31 August ATDD-06 (Product PR-ASS-1) Page 11 Fig Current coverage of COSMO-ME. Fig Envisaged coverage for product PR-ASS-1. The top model layer should be raised to a minimum of 31 km to improve the simulation of synthetic radiances. The elevation of the top model layer will involve the following steps: introduction of new model layers consistent with numerical stability requirements; test of the new operational configuration.

12 Algorithms Theoretical Definition Document, 31 August ATDD-06 (Product PR-ASS-1) Page Algorithms description The following Sections describe the algorithms used in the various modules of the precipitation products generation chain. The degree of detail is consistent with the requirement of a manageable document. Detailed algorithm descriptions are available within the H-SAF project inside an electronic forum at the site: ftp://ftp.meteoam.it - username: hsaf - password: 00Hsaf hsaf algorithm-forum. 4.1 Quantitative Precipitation Forecast PR-ASS-1 will be generated as ordinary evolution of the Quantitative Precipitation Forecast (QPF) effort of CNMCA, and include precipitation rate and accumulated precipitation. The Quantitative Precipitation Forecast (QPF) for H-SAF will be a special output of the NWP operational chain run by the Centro Nazionale di Meteorologia e Climatologia Aeronautica (CNMCA). Several NWP models are available. For the purpose of H-SAF, the COSMO-ME NWP Model will be utilised, after appropriate tailoring to the H-SAF requirements. In most NWP models the majority of the clouds, especially convective clouds, can not be resolved by the grid mesh, therefore moist processes (turbulent fluxes and sinks/sources) need to be parameterized. The treatments of moist processes in a NWP model may be divided into two categories: microphysical processes or grid-scale clouds and precipitation parameterization cumulus parameterization Consequently, the precipitation is partitioned into two fractions: the grid-scale precipitation from the microphysical processes parameterization: that occurs upon saturation of the air within the model grid boxes and thus is often referred to as explicit condensation; the convective precipitation from the cumulus parameterization: which is devised to capture the sub-grid scale cumulus convection; Generally, convective parameterization is applied at conditionally unstable grid points, while explicit condensation at saturated grid points and excess moisture is eliminated through condensation and heating. The partitioning into the components depends on the mesh size. As the grid spacing decreases an increasing fraction of the circulation features connected to convective systems will be resolved at the grid scale. The term grid-scale precipitation generally refers to the production of precipitation and the accompanying latent heat release, via atmospheric processes that may be resolved in a NWP model such as areas where upward motion will ultimately lead to clouds and precipitation. The primary interest in the numerical modelling of grid-scale clouds and precipitation is the behaviour of the overall ensemble of particles. 4.2 The cloud-precipitation module The mathematical description of the overall evolution of a cloud, in which any combination of the water categories with corresponding microphysical processes may be present simultaneously in the context of the changing airflow, is based on budget equations for the water substances. These equations allow to predict numerically the water mass in each category, as it changes due to advection, turbulent diffusion, sedimentation and various microphysical sources and sinks throughout the evolving cloud. The resulting system of equations is also often referred to as water-continuity model. Three basic strategies may be used to represent cloud microphysics in a numerical meteorological model: spectral, bulk and multiplemoment water-continuity models. A bulk water-continuity model is used in COSMO Model (Doms et al. 2004), because this scheme is computationally cheaper than the other two approaches. The basic idea of this method is to assume as few categories of water as possible and to predict directly the total mass fraction qx in each category in order to minimize the number of equations and calculations. To accomplish this simplification, the

13 Algorithms Theoretical Definition Document, 31 August ATDD-06 (Product PR-ASS-1) Page 13 shapes and the size distributions of particles must be assumed and the microphysical processes must be parameterized in terms of the specific content of the water categories qx. The non-precipitating water categories are usually supposed to be monodisperse whereas the precipitation particles are assumed to be exponentially distributed in size with respect to particle diameter as spectral coordinate. Presently the so-called "two-category ice scheme" (Doms 2002; Baldauf and Schultz 2004) is switched on in COSMO-ME runs. This parameterization considers water vapour, cloud water, cloud ice, rain and snow as prognostic variables in the hydrological cycle (Fig. 06) and allows for the simulation of precipitation formation in water, mixed-phase and ice clouds. In the near future a three category ice scheme (Reinhardt and Seifert, 2006) comprising graupel will be implemented. Fig Cloud microphysical processes considered in the two-category ice scheme. The cumulus parameterization is used in NWP to predict the collective effects of (many) convective clouds that may exist within a single grid element. It relates unresolved effects (convection) to gridscale properties using statistical or empirical techniques. All NWP models with grid spacing larger than that of individual thunderstorms or storm clusters need to parameterize the effect that convection has on larger-scale model variables in each grid element. Cumulus parameterizations are basically classified in: adjustment schemes: nudge the vertical profile toward an empirical reference profile; mass-flux schemes: use simple cloud model to simulate rearrangements of mass in a vertical column. The COSMO-ME model having a 7 km grid spacing uses a cumulus parameterization; in particular the Tiedtke mass-flux scheme is switched on. In the mass-flux schemes the effects of the clouds on the resolvable-scale variables are parameterized in terms of the convective mass fluxes and the convection is assumed to influence the environment through environmental subsidence and detrainment at the top of the updraft or the bottom of the downdraft. In the Tiedke scheme a 1-dimensional cloud model is closed by making convection (triggering and intensity) dependent on the moisture supply by large-scale

14 Algorithms Theoretical Definition Document, 31 August ATDD-06 (Product PR-ASS-1) Page 14 flow convergence and boundary layer turbulence. The vertical distribution of heating and drying is estimated using the cloud model to satisfy the constraints on intensity. Column equilibrium is supposed for precipitation formed in convective clouds where the source/sink terms include the conversion of cloud water to form rain, the evaporation of rain in the downdraft and below cloud base. 4.3 Algorithm validation/heritage COSMO-ME is continuously maintained and improved through communication and feedback between the modelling and the user community. The model performance is evaluated for both upper air and surface parameters through comparison with conventional and radar observations. An update on verification results for COSMO-ME (previously EURO-LM) can be accessed online at: Validation results of precipitation parameterization can be found in the references noted in section 6.3. The grid-scale precipitation scheme has been refined and tuned in recent work by Seifert 2008, at

15 Algorithms Theoretical Definition Document, 31 August ATDD-06 (Product PR-ASS-1) Page Examples of PR-ASS-1 products Fig. 07 and Fig. 08 show examples of PR-ASS-1 products, a 24-hour accumulated precipitation map and a map of instantaneous precipitation, respectively. It is noted that the product does not cover the full H-SAF area. However, the area will be progressively extended in the course of CDOP. Maps are in equal latitude/longitude projection. The products result from the forecasting run started at a T 0 conveniently in advance so as to enable the output to be sufficiently stabilised. The accumulated precipitation in the first figure refers to the previous 24 h. Fig hour accumulated precipitation from COSMO-ME for 20 Apr 2010, 00 UTC. Forecast run initialised at 00 UTC of 19 Apr Fig Instantaneous precipitation from COSMO-ME for 20 Apr 2010, 00 UTC. Forecast run initialised at 00 UTC of 19 Apr 2010.

16 Algorithms Theoretical Definition Document, 31 August ATDD-06 (Product PR-ASS-1) Page 16 References Baldauf M. and J.P. Schultz, 2004: Prognostic precipitation in the Lokal Modell (LM) of DWD. Cosmo Newsletter, No. 4, Available on line at Davies H.C. and R.E. Turner, 1977: Updating prediction models by dynamical relaxation: an examination of the technique. Quart. J. Roy. Meteor. Soc., 103, Doms G., 2002: The LM cloud ice scheme. Cosmo Newsletter, No. 2, Available on line at Doms G., J. Forstner, H. Heise, J. Herzog, M. Raschendorfer, R. Schrodin, T. Reinhardt and G. Vogel, 2004: A Description of the Nonhydrostatic Regional Model LM - Part II Physical Parameterization. Available on line at Forstner J. and G. Doms, 2004: Runge-Kutta time integration and high-order spatial discretization of advection: a new dynamical core for LM. COSMO Newsletter, No 4, Jacobsen I. and E. Heise, 1982: A new economic method for the computation of the surface temperature in numerical models. Contr. Atmos. Phys., 55, Lott F. and M.J. Miller, 1997: A new subgridscale orographic drag parameterization: Its formulation and testing. Quart. J. Roy. Meteor. Soc., 123, pp Lynch P., D. Girard and V. Ivanovici, 1997: Improving the efficiency of a digital filtering scheme. Mon. Wea. Rev., 125, Reinhardt T. and A. Seifer, 2006: A three category Ice Scheme for LMK, Cosmo Newsletter, No. 6, Available on line at Ritter B. and J.F. Geleyn, 1992: A comprehensive radiation scheme for numerical weather prediction models with potential applications in climate simulations. Mon. Wea. Rev., 120, Schrodin R. and E. Heise, 2001: The multi-layer version of the DWD soil model TERRA-LM. COSMO Technical Report, No.2 (available at Seifert A., 2008: A Revised Cloud Microphysical Parameterization for COSMO-LME. Available at Skamarock W.C. and J.B. Klemp, 1992: The stability of time-split numerical methods for the hydrostatic and the non-hydrostatic elastic equations. Mon. Wea. Rev., 120, Thomas S., C. Girard, G. Doms and U. Schaettler, 2000: Semi-implicit scheme for the DWD Lokal- Modell. Meteorol. Atmos. Phys., 82, Tiedke M., 1989: A comprehensive mass flux scheme for cumulus parameterization in large school models. Mon. Wea. Rev., 117, Wicker L. and W.C. Skamarock, 1998: A time-splitting scheme for the elastic equations incorporating second-order Runge-Kutta time differencing. Mon. Wea. Rev., 126,