Numerical weather prediction

Numerical weather forecasts are computer-based weather forecasts. (: Thermal equation of state of ideal gases, first law of thermodynamics, continuity equation, Navier -Stokes equations in the core ), the state calculated at later times from the state of the atmosphere at a given initial time point is determined by numerical solution of the relevant equations. These calculations include some cases more than 14 days and are the basis of all modern weather forecasting.

Operation

In such a numerical prediction model the computational domain with grid cells and / or by a spectral representation is discretized so that the relevant physical quantities, such as particularly temperature, pressure, density, wind direction and wind speed, in three-dimensional space and as a function of time can be represented. The physical relationships that describe the state of the atmosphere and its variation are modeled as a system of partial differential equations. This dynamic system is solved approximately using methods of numerical analysis, which are usually implemented as computer programs in Fortran. Supercomputers are for this purpose because of the large expense often used. It is generally between global models ( mesh size approximately 10-50 km ), the computational domain covers the entire globe and local or neck models ( briefly also LAM for limited area model) differed. The latter are usually higher resolution (now approximately 1-15 km mesh size) expected only in a limited area. To then determine the values ​​at the edge of the model area during the forecast statement makes sense, usually interpolated results of a global model or larger area, limited area model used (so-called " nesting ").

Parameterizations

Relevant processes that are small-scale model than the mesh size and are not included in the above mentioned system of equations must be parameterized. The parameterizations describe the effect of these processes on the processing parameters on the model grid using simplifying assumptions and are an integral part of the model code. Typical parameterizations are: cloud microphysics (formation and alteration of cloud and precipitation particles ), radiation, turbulence, floor model, schemes for shallow and deep convection.

Data assimilation

In addition, the determination of the initial state of the model atmosphere has an important significance for the success of the model prediction. This involves using various mathematical methods ( variational methods such as 3D, 4D -Var, Optimal interpolation, nudging, Kalman filter) a weighted combination of measurements and older model predictions to the model grid interpolated ( so-called data assimilation ). Measured sizes of remote sensing devices (radar, lidar, satellite ) have to be transformed into model variables and vice versa. Conventional measurements of temperature, humidity, pressure, etc. of weather stations, weather balloons, aircraft, ships and buoys must simply be interpolated spatially and temporally. In addition, incorrect measurements have to be selected and systematic measurement error (bias ) are corrected.

History

The possibility of numerical weather prediction has been demanded for the first time in 1904 by Vilhelm Bjerknes in a lecture without that he could show a concrete way. Lewis Fry Richardson calculated during the First World War for the first time, a weather forecast, and even if the result was grotesquely wrong, could be built after the invention of the computer on its preparatory work. John von Neumann then proposed in 1946 to use the computer for this purpose. In March 1950, ENIAC calculated for the first time, a weather forecast from actual weather data. Due to the increasing computing resources and new knowledge in the field of meteorology and numerical analysis since the resolution and quality of the model predictions could be continuously improved. More and more weather services in developing and emerging countries now operate their own numerical predictions, or at least use numerical products.

Small-scale forecast

The calculated from the models weather forecasts are often inaccurate for predicting the weather "on the spot " due to the limited model resolution, the uncertainty in the initial conditions and the non-linear trends in the atmosphere ( "chaos" ). The calculated values ​​are therefore usually checked by meteorologists on plausibility, compared with empirical values ​​and transformed into forecast texts and weather warnings.

Model Output Statistics ( MOS) is an approach to automated small-scale weather forecast. Here, the data provided by the models are set in relation to statistical measurement series in order to provide an accurate prediction as possible " on site". In contrast, the data provided are only interpolated for the desired locations in the Direct Model Output ( DMO).

Ensembles

Because of the chaotic nature of the weather, in many cases, a slight change in the output data, in particular for medium -and long -term predictions lead to a complete change in the forecast ( Butterfly Effect). Therefore, in addition to the so-called main run in which the computer with the actual measured values ​​to be fed, more runs were conducted in which authors work with slightly different data and a somewhat coarser resolution of the model grid points. Thus, the forecast uncertainty is to be estimated. The results of these runs are compared in ensembles. If the results for a period of prognosis similar, so that's an indication that the forecast for this period is relatively safe. While in some cases the weather situation thus over 10 days is quite easy to predict, there are other cases in which after a few days, a satisfactory prediction is hardly possible. The initial perturbations for the individual ensemble members are using random ( stochastic ) disturbance, disruption of assimilated observations to account for the measurement error (ensemble data assimilation ), disturbance in the direction of greatest sensitivity to interference by means of so-called singular vectors or rescaling of divergence of earlier predictions ( breeding ) is generated. More recently, the uncertainty in the parameterizations during the model integration is by interfering with the calculated values ​​contained therein considered ( stochastic model physics ). Global ensemble models are created, for example, the ECMWF, UK Metoffice, NCEP in the U.S. and in Canada. Ensembles with high-resolution cut models like the COSMO - DE- EPS of the German Weather Service are only a few years of use and are still the subject of intense research.

Models

There are a variety of models of the various weather services. These use different numerical methods, grid and parameterizations and may vary significantly in their prediction from each other. The models are usually recalculated at least once a day and start to the Synoptic main dates 0, 6, 12, 18 UTC clock.

Among the best known models include the global model GFS (Global Forecast System, formerly AVN) of the U.S. NOAA. It calculates four times daily predictions. The GFS data are freely available and are therefore used mainly by small weather services.

JRC is divided into three sub - models, of which the most detailed, supplies forecasts for every three hours of the next 3.5 days and a grid resolution of 40 km has. The long-term part - model ranges to 16 days in the future, the weather forecast, but only for every twelve hours and has a lower resolution.

Other well-known global models are:

  • GME (Global Model Europe): Since 1999, global model of the German Weather Service on an icosahedron -A- Grid
  • ICON ( icosahedral non- hydrostatic global circulation model ): New generation model of the German Weather Service and the Max Planck Institute for Meteorology (in development ) on an icosahedral C- grid
  • UM ( Unified Model ) of the UK Met Office Met Office UKMO (Can be used globally as well as a detail model)
  • IFS (Integrated Forecast System ): spectral global model of ECMWF (European Centre for Medium-Range Weather Forecasts)
  • GEM: a global model of the Canadian Meteorological Service
  • Arpege: spectral global model of the French weather service Meteo France with variable resolution within the model area
  • GSM: Global Spectral Model of the Japanese Meteorological Service
  • NOGAPS: global model of the U.S. Fleet Numerical Meteorology and Oceanography Center

Neck models ( LAMs ) are, for example:

  • MM5 Mesoscale Model 5; very common at universities now increasingly replaced by WRF
  • ETA Model Serbia, USA
  • WRF Weather Research and Forecasting Model USA (code freely available)
  • COSMO model (formerly called " Local Model " LM / LME / aLMo ): Extract model of the German Weather Service and the COSMO consortium ( including Meteo Switzerland, Italy, Russia, Romania, Greece)
  • ALADIN ALARO - AROME: Spectral cut- weather prediction model family of Météo -France, the ZAMG (Vienna), the CHMI ( Prague) and many other European Meteorological Services
  • HIRLAM: widespread in Scandinavia, the Netherlands, Ireland and Iceland ( hydrostatic spectral model )

Demarcation for climate modeling

Climate models have basically the same structure as weather prediction models ( discretization on a grid or in the spectral space, numerical solution of the same physical equations, parameterizations ). There are also global and neck models. However, the forecast is objective (average state of the atmosphere for decades ( climate) versus exact as possible state of the atmosphere in the next few hours or days (weather) ) is different, which leads to slight variations in the design. The weather forecast of the knowledge of the initial state (initial value problem) plays an important role by means of data assimilation. The details of individual weather situation, however, disappear by the time average of Lung in climate models. These, however, require a precise knowledge and future projection of the change in external drives ( boundary value problem) such as variations in solar radiation, ocean temperature (which is why frequent coupling with an ocean model) or the atmospheric composition (aerosols, greenhouse gas emissions from natural and artificial sources ), the soil (change of vegetation by agriculture with implications for the radiation and the water cycle ) etc.. too in climate modeling is the ensemble technique popular, where the main focus is on the estimation of the uncertainty of the said external drives is (scenarios ) defined by the (unknown ) future human behavior (land use, emissions) can be influenced. In addition, the implementation of the physical conservation laws in the model ( conservation of mass, conservation of energy ) is of greater importance due to the long calculation times. Performs the approximate solution of the equations by discretization, for example to a minimal systematic change of the atmospheric mass, so this is on a scale of a few hours ( weather model ) often hardly relevant, while the effect in the invoice for centuries ( climate model ) can add up dramatically. The long computation times often require compromises in the resolution of climate models ( coarse mesh), which in turn can lead to differences in the processes to be parameterised. However, some numerical models - for example, ICON, COSMO and ALADIN - are used for both weather prediction and climate bills.

Dynamical system National Centers for Environmental Prediction Deutscher Wetterdienst MM5 (weather model)
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