Numerical Weather Forecasting also called Numerical weather prediction (NWP) is a weather forecasting technique or the science of predicting the weather using a mathematical equation that describes virtually all dynamic and physical processes in the atmosphere and ocean using numerical procedures and computational techniques. 

These mathematical equations are translated into computer codes and uses numerical method and parameters of other physical processes combined with their initial and boundary condition before being tested in a geographic area.

Brief History

The first attempt at Numerical weather prediction (NWP) was in the 1920s by Lewis Fry Richardson but it was until the advent of computer simulation in the 1950s that numerical weather predictions produced a realistic result.

In the 1920s, Lewis Fry Richardson adopted a procedure originally developed by Vilhelm Bjerknes to produce by hand a six-hour forecast for the state of the atmosphere over two points in central Europe, taking at least 42 days (approximately six weeks) to do so.

Richardson foresaw a “forecast factory,” where he calculated that 64,000 human “computers,” each responsible for a small part of the globe, would be needed to keep “pace with the weather” in order to predict weather conditions. They would be housed in a circular hall like a theatre, with galleries going around the room and a map painted on the walls and ceiling. A conductor located in the centre of the hall would coordinate the calculations using coloured lights.

The prediction turned out to be completely unrealistic, but his efforts were a glimpse into the future of weather forecasting. It was not until the coming into being of computer and computer simulations that computation time was decreased to less than the forecast period itself.

As computers evolved and got more powerful during the years, newer atmospheric models were been developed to take advantage of the added available computing power. These newer models include more physical processes in the simplifications of the equations of motion in numerical simulations of the atmosphere.

Initialization and Parameterization

The atmosphere as we all know is fluid, and as such, the concept of numerical weather prediction is to sample the state of the fluid at a given time and use the equations of fluid dynamics and thermodynamics to estimate the state of the fluid at some time in the future. The process of entering observation data into the model to generate initial conditions is called Initialization.

In the same way, some meteorological processes (i.e processes involved in the science of weather or weather forecasting) are too small-scale or too complex to be explicitly included in numerical weather prediction models, therefore parameterization is adopted. A procedure for representing these processes by relating them to variables on the scales that the model resolves is called Parameterization.


However, even with the accelerating power of supercomputers, the forecast skill of numerical weather models still gets difficult at some point due to certain factors.

  • The amount of available data
  • The time available to analyze it
  • The complexity of weather event

Furthermore, there are also factors affecting the accuracy of numerical predictions, these factors include the density and quality of observations used as input to the forecasts. This is because numerical weather models are only representations and approximations of reality. They don’t account for all the variables (factors) that may affect the weather.

Alongside the factor affecting the accuracy of numerical predictions is the deficiencies in the numerical models. Although post-processing techniques such as model output statistics (MOS) have been developed to improve the handling of errors in numerical predictions, there will always be slight errors in forecasting. 

This is because the Earth’s atmosphere is highly complex; the main problem resides in the chaotic nature of the partial differential equations that govern the atmosphere. Small errors grow with time, doubling about every five days. Getting to understand this shows that this chaotic behaviour limits accurate forecasts to about 14 days. 

Furthermore, the partial differential equations adopted in the model need to be supplemented with parameterizations for solar radiation, moist processes (clouds and precipitation), heat exchange, surface water, and the effects of terrain.

How Does NWP Work?

Weather models use systems of differential equations based on the laws of physics, and use a coordinate system which divides the planet into a 3D grid. Wind, heat transfer, solar radiation, relative humidity, phase changes of water and surface hydrology are calculated within each grid cell, and the interactions with neighbouring cells are used to calculate atmospheric properties in the future.

Mathematical models based on the same physical principles can be used to generate either short-term weather forecasts or longer-term climate predictions.

For instance, the Kanda weather group launches weather balloons carrying radiosondes into the atmosphere. These radiosondes are battery-powered telemetry devices that measure altitude, pressure, temperature, relative humidity, wind and cosmic ray at high altitudes. They make accurate measurements of atmospheric parameters above the surface and these data are received and inputted into a Machine Learning (ML) model that correlates this weather data at different heights and calculates the atmospheric property to make a weather forecast. 

However, in order to control or manage the vast datasets gotten during initialization and perform the complex calculations required during numerical weather prediction, some of the most powerful supercomputers in the world are being used.

Models used in NWP

Some of the models used in Numerical Weather forecasting are;

  • NASA MERRA-2 from 1980 till present
  • NCEP Climate Forecast System Reanalysis (CFSR) from 1979 till present
  • NCEP/DOE Reanalysis AMIP-II (R2) from 1979 till present
  • NCEP/NCAR Reanalysis I (R1) from 1948 till present.

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