Global model GME

Grid structure of GME and its construction

DWD is one of the 14 weather services worldwide running a global weather forecast model. All the other national weather services with modelling activities restrict themselves to regional models which predict the weather for a certain geographical area (LAM: Limited Area Model) only. Such models need the forecasts of global models as lateral boundary conditions.

GME is the first operational weather forecast model which uses an icosahedral-hexagonal grid covering the globe. In comparison to traditional grid structures like latitude-longitude grids the icosahedral-hexagonal grid offers the advantage of a rather small variability of the area of the grid elements. Moreover, the notorious ’pole-problem’ of the latitude-longitude grid does not exist in the GME grid.

The macro-triangulation of the GME grid is based on an icosahedron inscribed in the sphere. Two of the twelve vertices of the icosahedron coincide with the north and south poles. Connecting the twelve vertices by great circle arcs, 20 large spherical triangles are formed with an edge length of 7054 km. By iteratively sub-dividing these large triangles into smaller ones a grid of the required resolution can be derived. The grid spacing of the resulting grid is defined as the mean edge length of the smallest spherical triangles; currently the grid spacing of GME is 40 km. The vertices of the triangles which form the grid points are surrounded by six (five at the 12 special points of the original icosahdron) triangles. The grid points are therefore the centres of spherical hexagons or pentagons. The GME grid approximates the sphere by many hexagons (368630 at a grid spacing of 40 km) and exactly 12 pentagons.

The mean size of a grid element is 1384 km2 at the current grid spacing of 40 km. All model variables like pressure, temperature, wind components, water vapour, cloud water and cloud ice are defined as mean values over the area of a grid element (i.e. over 1384 km² ; this also applies for the external parameters such as orography, see figure). Therefore GME cannot resolve many local details of the topography which may have an important influence on the local weather. To forecast such local effects, e.g. the channelling of the flow in the Rhine valley or the land-sea breeze circulation at the coasts of the North Sea or the Baltic Sea, is the task of the higher resolution model COSMO-EU with a grid spacing of 7 km.

comparison of orography with 1 km and 40 km resolution

Orography in an area containing 7 GME grid points around Mont Blanc. Left: raw data with 1 km resolution (maximum height: more than 4000 m a.s.l.); right: GME orography derived from the raw data as mean values each over the area of a single grid element of 1384 km2 (maximum height: less than 2500 m a.s.l.).

The main prognostic variables of GME are surface pressure, horizontal wind components, temperature, specific contents of water vapour, cloud water and cloud ice and ozone on 40 model layers in the atmosphere from the surface up to a height of approximately 31 km. Thus the atmosphere is resolved by 368642 x 40 ~ 15 Million grid points in GME. For land grid points the temporal evolution of temperature and the contents of soil water and soil ice at seven layers is predicted, too, as well as the water content and mean density of a snow cover. Over the oceans, if not covered by sea ice, the sea surface temperature, analysed once a day, is kept constant throughout the forecast range. At sea ice points an ice model predicts temperature and thickness of the sea ice.

Diabatic processes like radiation, turbulence, cloud formation and precipitation play an important role in weather forecasting in addition to the so-called adiabatic processes like the horizontal and vertical transport processes in the atmosphere. The main goal of physical parameterisations is the proper description of the diabatic processes the scale of which is usually much smaller than the grid spacing of the weather prediction model.

Physical processes simulated by GME and the quantities that influence them and are influenced by them.

For the daily operational schedule of GME we have to distinguish between the data assimilation and forecast suites (see figure). To derive the initial state (analysis) of a GME forecast in the data assimilation suite, the 3-hour GME forecast valid at the analysis time (the so-called first guess) will be corrected by all observations available at this time. The analysis should – on average – be as close as possible to the (unknown) true state of the atmosphere. Four times daily the forecast suite provides predictions of the weather up to 174 hours (starting from 00 and 12 UTC analyses) or 48 hours (from 06 and 18 UTC analyses). A forecast day of GME takes about 15 minute wall clock time on DWD’s supercomputer, and a 7-day forecast corresponds to about 50 GByte of data. For the first 78 hours the forecast fields are stored at hourly intervals because they serve as lateral boundary conditions for the regional model COSMO-EU, too; beyond 78 hours a three-hour time interval is used. In addition to the above mentioned prognostic variables, a variety of other quantities are derived diagnostically and made available to the users (see model products).

Daily operational schedule of the NWP at DWD. GME-T und COSMO-EU-T denote test suites which are used to compare new versions of the models (and / or the data assimilation) with the operational analyses and forecasts.

The GME forecasts provide the meteorological input to many applications like ocean wave prediction or global dispersion modelling for nuclear or chemical species as part of emergency preparedness systems in case of accidents in nuclear or chemical plants.

Additionally to these internal applications many external users need GME forecasts as input to their products, e.g. the regional hydrological authorities use precipitation forecasts in their models for water level and flood prediction, and the BSH (Federal Maritime Authority, Hamburg) uses the wind forecasts to predict storm surges and water level at the German coasts.

Finally, more than 20 weather services worldwide (e.g. most of the COSMO partners (Greece, Italy, Poland, Romania and Switzerland) as well as many emerging and developing countries like Botswana, Brazil, China, Israel, Kenya, Mozambique, Oman, Philippines, Senegal and Vietnam) use the GME forecasts which are transferred via the internet as lateral boundary conditions for their limited area models (e.g. HRM).