Numerical weather forecast – assessment of the atmosphere in the future based on the knowledge of initial conditions and forces acting on the air. The numerical weather forecast is based on solving the air motion equations using their discretization and using mathematical machines for calculations.

# Numerical weather prediction

The initial state of the atmosphere is determined on the basis of simultaneous measurements all over the globe. The equations of the air particles’ motion are introduced assuming that the air is a liquid. These equations can not be solved in a simple way. The key simplification, requiring the use of computers, is the assumption that the atmosphere can be described roughly as many discrete elements influenced by various physical processes. Computers are used to calculate changes in **air temperature**, **air pressure**, humidity, flow velocity and other values describing the air element. Changes in these physical properties are caused by various types of processes, such as heat and mass exchange, rainfall, movement over mountains, air friction, convection, the influence of solar radiation, and the impact of interaction with other air particles. Computer calculations for all elements of the atmosphere give the state of the atmosphere in the future, i.e. the **weather forecast**.

The discretization of air motion equations uses numerical methods of partial differential equations – hence the name of the **numerical weather forecast**.

## Numerical weather prediction models

The results from individual forecasting models, although calculated on the basis of the same data, differ because it is impossible to describe the processes taking place in the atmosphere, especially those with a very small range, in an unambiguous manner enabling reliable forecasting of their course. This is for many reasons:

- the basis for each numerical forecast is the initial conditions prepared on the basis of the current forecast and the results of observations and measurements (also for example satellite). The measurement network (especially regarding the higher layers of the atmosphere) is not dense enough and each measurement is burdened with a specific error, therefore the initial condition is also burdened with unavoidable errors. The way of assimilating the input data to the model is important. The boundary conditions also have an effect on the results of calculations;
- it is necessary to parameterize, i.e. to simplify taking into account all these meteorological phenomena, whose size is less than or equal to the step of the computational grid, because the models „see” directly only those phenomena whose range is greater than the step of the grid;
- whereas the size (step) of the computational grid is limited and relatively large (eg 14 km, 7 km, 2.8 km);
- there are different ways of parameterizing subscale processes;
- the numerical solution of the equations has an influence on the quality of the results.

Currently, mainly global and mesoscale forecasting models are used.

The global model covers the northern hemisphere with its range. The mesoscale model covers the area of one or several countries, and the grid step of this model now varies from 7 to 2 km. There are also regional models.

The frequency and presentation of results from the model depends on the findings. The most common time step for the visualization of results is from 1 to 3 hours in the mesoscale model, and in the operational work, the synoptics also use 12 and 24 hours for some elements.

As a result of numerical calculations, field forecasts for elements such as air temperature, pressure, humidity, wind, rainfall, cloudiness, convection indices and many other specialist parameters are obtained for various atmosphere levels.

The numerical forecast does not contain subjective elements. The obtained results are presented graphically in the form of numerical values in nodes of the grid, isolines, graphs, meteograms, weather icons.