About this page
Numerical Weather Prediction (NWP),is a computer simulation of the atmosphere and the basis of all forecasts used by sailors.
Related pages
On this page 
 How the Atmosphere works
 Calculating it
 Operational forecasting
 Forecast Ensembles
 A future problem
 Climate models
Introduction
Weather forecasting is in its third phase.
 For thousands of years single observer forecasting was the only possible tool.
 From the late 1850s, the synoptic approach let forecasters "look" at the weather as plotted and analysed on charts. They learned how to interpret and predict but only in a subjective manner.
 The third phase is the era of large computing systems and satellite observing technologies. This has made possible the development of NWP
How the Atmosphere Works
A simplified description of how the weather machine works is as follows:

Some of these processes are illustrated in this diagram:
(From IPCC AR5, Woking Group 1 Report, Chapter09_FINAL.pdf Chapter 9, 1913.)
All these processes can be expressed in mathematical equations. At the centre of these equations is one that says, in effect, that applying a force results in change – acceleration or deceleration. This is Newton’s third law.
There are always forces in the atmosphere – gravity, the Coriolis effect and pressure gradients. Consequently, there is always change; further, pressure gradients are always changing so that the atmosphere is always in a state of flux.
Calculating it
Physicists call weather forecasting an initial value problem. At the initial time, T=0, the rates of change of each weather element can be calculated. That allows estimates to be made a short time, minutes ahead, of winds, temperatures, pressures, water vapour and liquid water. These new values then provide a new starting point to calculate for the next few minutes.
The start of any weather forecast is an analysis of current conditions. There are many sources of data used in NWP and these have different characteristics in the way they represent the atmosphere. There are differences in accuracy, resolution, numbers of data of various kinds and differences in times that the measurements were made.
Bringing all these data together cannot be done precisely. There will always be uncertainties in the analysis detail.
After analysis, the forecast calculations can begin using massive computers such as this one used by the ECMWF and the U K Met Office and capable of thousands of billions of sums per second.
However, even that power is miniscule compared to the atmosphere. Many approximations have to be used and many terms are estimates.
One of the “approximations” is to represent the atmosphere by values on a 3dimenional grid.
The UK Met Office global grid has a spacing of 1/8 degree, about 17km in the horizontal. There are1,769,472 grid point with, 70 levels at each from 20 m to 80 km above the surface of the earth.
A limitation of any Grid is that weather and topography can only be defined on a size of about 5 grid lengths.
Operational forecasting
The UK Met Office runs its NWP models on a 6hourly basis. Forecasts for the first 6 hours of the last run the ,last run are combined with all the observational data received over that period to produce the starting point for the next forecast.
In order to meet deadlines, there has to be a data cutoff time. Data arriving after that time are used later to recompute the first 6 hours’ forecast so getting the best start possible for the following run.
Limited area or mesoscale models are run in the same way. All this is on a “best endeavours” basis and users should always bear in mind the limitations to forecast accuracy.
Chaos and Forecast Ensembles
Chaos is always a problem – it has been suggested that a butterfly flapping its wings could lead to major weather systems. In fact, it cannot but small disturbances may grow into large ones.
There are always uncertainties in detail of weather analyses. These lead to uncertainties in the deterministic forecast. Hh
Model ensembles are a way of tackling this problem. After running the forecast model, small variations can be put into the analysis that are compatible with the original data. The forecast can be run many times and a spread of results obtained. The spread of these indicates the degree of uncertainty in the deterministic forecast..
A future problem
The amount of information that can be provided is enormous and access by users will become an increasing problem. How many sailors will have the ability to assess outputs from an ensemble? How many will want to spend the time needed to do so?
When will high speed communications become affordable for access over radio systems?
One thing is certain and that is that the written or spoken word will not and cannot cope with all the variations in the weather that exist, whether they are well forecast or not.
Seasonal, Decadal and Climate models
The UK Met Office uses the same basic model to study prediction on longer time scales including climate prediction. These models are run with some differences. First, grid lengths and time steps are increased while number of levels and depth of models are decreased. For climate purposes, grids are about140 km with 40 levels
More importantly, there are factors that are, effectively constant over periods of a few days but which can change over longer periods. These include
 Changes in greenhouse gas concentrations.
 Changes in land use.
 Two way effects of atmosphere on ocean temperatures and currents
 Dust concentrations.
 Solar radiation.
 Polar ice cover.
In addition, the effects of random events such as volcanoes can be studied. For seasonal up to decadal prediction the effects of El Niño and La Niña can be investigated.
More Reading on this site
Met Office Pages
The Internet has a wealth of pages of varying degrees of complexity. Try putting "numerical models" into the Met Office page search engine.. Then do the same with Google.