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The miracle of numerical weather forecasting: How to use mathematical models to predict future weather?
With the advancement of science and technology, the development of meteorology has enabled us to better understand the Earth's climate system. Numerical Weather Prediction (NWP) is a successful example of applying mathematical models to weather forecasting. Through observational data, these models can predict future weather, bringing great convenience to people’s daily lives.
The goal of numerical weather forecasting is to use current meteorological observations to predict future weather conditions, a process that relies on computers running highly complex mathematical models.
History of Numerical Weather Forecasting
The roots of numerical weather prediction can be traced back to the 1920s, when meteorologist Louis F. Richardson first proposed the use of mathematical models to make forecasts. However, due to the lack of computing power at the time, the process was so cumbersome that it took Richardson six weeks to complete a six-hour forecast for two points in central Europe. It was not until the 1950s, with the birth of the ENIAC supercomputer, that the efficiency of data computing was greatly improved, making numerical forecasting feasible and practical.
In 1954, Cole-Gustav Rossby's team at the Swedish Meteorological and Hydrological Institute successfully conducted the first operational forecast, marking the official entry of numerical weather forecasting into the practical stage.
Basic principles of numerical forecasting
The core of numerical weather forecasting lies in a variety of computational models, which use current meteorological data to predict future weather based on the basic laws of fluid mechanics and thermodynamics. The observation data mainly come from meteorological satellites, weather balloons and ground-based meteorological stations. These data are processed by data assimilation technology to generate the initial conditions of the model.
Weather models process tens of terabytes of data when generating forecasts, requiring the use of the world's most powerful supercomputers.
Mathematical Model and Calculation Method
In numerical predictions, the equations used are called primitive equations, which are composed of nonlinear partial differential equations that can describe the dynamic characteristics of the atmosphere. The solutions to these equations cannot be completely obtained by traditional analytical methods, so numerical methods are needed to approximate them.
Numerical models typically rely on finite-difference or spectral methods to perform their calculations, which are able to take into account a wide range of physical processes in the atmosphere.
Forecast accuracy and limitations
Although modern numerical weather prediction techniques have improved significantly, current forecast capabilities are limited to approximately six days, primarily because small errors grow more severe over time, typically doubling within five days. This is due to the chaotic nature of the atmosphere.
The development of integrated forecasting
In order to deal with the uncertainty in prediction, ensemble forecasting has gradually become mainstream since the 1990s. This method uses multiple forecast models for calculations and analyzes the statistical characteristics of the results to improve the accuracy and reliability of the forecast.
Ensemble forecasts allow meteorologists to better assess forecast uncertainties and extend the time horizon over which forecasts are valid.
Future Outlook
With the continuous advancement of computing technology, future numerical weather forecasts will be more accurate and able to capture smaller-scale meteorological phenomena. However, whether these technological advances can solve the current chaos problems remains a question worth exploring. Faced with the challenge of continued climate change on Earth, how can we intelligently use these predictive tools to adapt to future life?
