Ensemble forecasting
Encyclopedia
Ensemble forecasting is a numerical prediction method that is used to attempt to generate a representative sample of the possible future states of a dynamical system
. Ensemble forecasting is a form of Monte Carlo analysis
: multiple numerical predictions are conducted using slightly different initial conditions
that are all plausible given the past and current set of observations, or measurements. Sometimes the ensemble of forecasts may use different forecast models for different members, or different formulations of a forecast model. The multiple simulations are conducted to account for the two sources of uncertainty in weather forecast models: (1) the errors introduced by chaos
or sensitive dependence on the initial conditions; and (2) errors introduced because of imperfections in the model, such as the finite grid spacings. Ideally, the verified weather pattern should fall within past ensemble spreads, and the amount of spread should be related to the probability of certain weather events occurring.
Considering the problem of numerical weather prediction
, ensemble predictions are now commonly made at most of the major operational weather prediction facilities worldwide, including the National Centers for Environmental Prediction
(US), the European Centre for Medium-Range Weather Forecasts
(ECMWF), the United Kingdom Met Office
, Meteo France, Environment Canada
, the Japanese Meteorological Agency, the Bureau of Meteorology
(Australia), the China Meteorological Administration
, the Korea Meteorological Administration
, and CPTEC (Brazil). Experimental ensemble forecasts are made at a number of universities, such as the University of Washington, and ensemble forecasts in the US are also generated by the US Navy and Air Force. There are various ways of viewing the data such as spaghetti plots, ensemble means or Postage Stamps where a number of different results from the models run can be compared.
, owing to the chaotic nature
of the fluid dynamics
equations involved. Furthermore, existing observation networks have limited spatial and temporal resolution (for example, over large bodies of water such as the Pacific Ocean), which introduces uncertainty into the true initial state of the atmosphere. While a set of equations, known as the Liouville equations
, exists to determine the initial uncertainty in the model initialization, the equations are too complex to run in real-time, even with the use of supercomputers. These uncertainties limit forecast model accuracy to about six days into the future.
Edward Epstein
recognized in 1969 that the atmosphere could not be completely described with a single forecast run due to inherent uncertainty, and proposed a stochastic
dynamic model that produced means
and variance
s for the state of the atmosphere. Although these Monte Carlo simulations
showed skill, in 1974 Cecil Leith revealed that they produced adequate forecasts only when the ensemble probability distribution
was a representative sample of the probability distribution in the atmosphere. It was not until 1992 that ensemble forecasts began being prepared by the European Centre for Medium-Range Weather Forecasts
and the National Centers for Environmental Prediction
. The ECMWF model, the Ensemble Prediction System, uses singular vectors
to simulate the initial probability density
, while the NCEP ensemble, the Global Ensemble Forecasting System, uses a technique known as vector breeding.
or varying initial conditions. The ensemble forecast is usually evaluated in terms of an average of the individual forecasts concerning one forecast variable, as well as the degree of agreement between various forecasts within the ensemble system, as represented by their overall spread. Ensemble spread is diagnosed through tools such as spaghetti diagrams, which show the dispersion of one quantity on prognostic charts for specific time steps in the future. Another tool where ensemble spread is used is a meteogram
, which shows the dispersion in the forecast of one quantity for one specific location. It is common for the ensemble spread to be too small to incorporate the solution which verifies, which can lead to a misdiagnosis of model uncertainty; this problem becomes particularly severe for forecasts of the weather about 10 days in advance.
varies substantially depending on such factors as the forecast model and the region for which the forecast is made.
Ideally, the relative frequency of events from the ensemble could be used directly to estimate the probability of a given weather event. For example, if 30 of 50 members indicated greater than 1 cm rainfall during the next 24 h, the probability of exceeding 1 cm could be estimated to be 60%. The forecast would be considered reliable if, considering all the situations in the past when a 60% probability was forecast, on 60% of those occasions did the rainfall actually exceed 1 cm. This is known as reliability or calibration. In practice, the probabilities generated from operational weather ensemble forecasts are not highly reliable, though with a set of past forecasts (reforecasts or hindcasts) and observations, the probability estimates from the ensemble can be adjusted to ensure greater reliability. Another desirable property of ensemble forecasts is sharpness. Provided that the ensemble is reliable, the more an ensemble forecast deviates from the climatological event frequency and issues 0% or 100% forecasts of an event, the more useful the forecast will be. However, sharp forecasts that are unaccompanied by high reliability will generally not be useful. Forecasts at long leads will inevitably not be particularly sharp, for the inevitable (albeit usually small) errors in the initial condition will grow with increasing forecast lead until the expected difference between two model states is as large as the difference between two random states from the forecast model's climatology.
for the benefit of society, the economy and the environment.
THORPEX establishes an organizational framework that addresses weather research and forecast problems whose solutions will be accelerated through international collaboration among academic institutions, operational forecast centres and users of forecast products.
TIGGE, the THORPEX Interactive Grand Global Ensemble, is a key component of THORPEX: a World Weather Research Programme to accelerate the improvements in the accuracy of 1-day to 2 week high-impact weather forecasts for the benefit of humanity. Centralized archives of ensemble model forecast data, from many international centers, are used to enable extensive data sharing and research. The designated TIGGE archive centers include the Chinese Meteorological Administration (CMA), The European Center for Medium-Range Weather Forecasts (ECMWF), and The National Center for Atmospheric Research (NCAR). Scientific data requirements and archive planning solidified in late 2005, and archive collection began in October 2006.
The Unidata LDM software package is used to transport the ensemble model data from the providers to the archive centers. Currently, the output from the ECMWF, UK Met Office (UKMO), CMA, Japan Meteorological Agency (JMA), National Centers for Environmental Prediction (NCEP-USA), Meteorological Service of Canada (CMC), Bureau of Meteorology Australia (BOM), Centro de Previsao Tempo e Estudos Climaticos Brazil (CPTEC), Korea Meteorological Administration (KMA), and MeteoFrance (MF) global models, totaling 440 GB/day, is moved at up to 30 GB/hour to NCAR (Realtime Statistics). By requirement the parameter fields, atmospheric levels, and physical units are consistent across all data from the providers and encoded in WMO GRIB-2 format. In contrast, each provider may submit their model output in a resolution they choose.
TIGGE data are available to the public for non-commercial research, with a 48-hour delay after forecast initialization time. At NCAR, users can discover data through the TIGGE portal and select parameters, grid resolution, and spatial subsets for the most current two-week period. The most current two-week period of TIGGE data are also available for direct download in the form of forecast files through the RDA near realtime 2-week TIGGE archive. Long term TIGGE data archives are available through the RDA full TIGGE archive. Forecast files are organized by level type (single level, pressure level, potential vorticity level, and potential temperature level), and forecast time-step for a specified model. All ensemble members are included in each forecast file. At ECMWF, users can discover and download data through a web interface linked to the Meteorological Archival and Retrieval System (MARS). CMA offers an additional option for CMA TIGGE data access. Each center will offer fast access to terabytes of data kept online and delayed access to the long term archives preserved in their archive systems.
The key objectives of TIGGE
Dynamical system
A dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each springtime in a...
. Ensemble forecasting is a form of Monte Carlo analysis
Monte Carlo method
Monte Carlo methods are a class of computational algorithms that rely on repeated random sampling to compute their results. Monte Carlo methods are often used in computer simulations of physical and mathematical systems...
: multiple numerical predictions are conducted using slightly different initial conditions
Initial value problem
In mathematics, in the field of differential equations, an initial value problem is an ordinary differential equation together with a specified value, called the initial condition, of the unknown function at a given point in the domain of the solution...
that are all plausible given the past and current set of observations, or measurements. Sometimes the ensemble of forecasts may use different forecast models for different members, or different formulations of a forecast model. The multiple simulations are conducted to account for the two sources of uncertainty in weather forecast models: (1) the errors introduced by chaos
Chaos theory
Chaos theory is a field of study in mathematics, with applications in several disciplines including physics, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions, an effect which is popularly referred to as the...
or sensitive dependence on the initial conditions; and (2) errors introduced because of imperfections in the model, such as the finite grid spacings. Ideally, the verified weather pattern should fall within past ensemble spreads, and the amount of spread should be related to the probability of certain weather events occurring.
Considering the problem of numerical weather prediction
Numerical weather prediction
Numerical weather prediction uses mathematical models of the atmosphere and oceans to predict the weather based on current weather conditions. Though first attempted in the 1920s, it was not until the advent of computer simulation in the 1950s that numerical weather predictions produced realistic...
, ensemble predictions are now commonly made at most of the major operational weather prediction facilities worldwide, including the National Centers for Environmental Prediction
National Centers for Environmental Prediction
The United States National Centers for Environmental Prediction delivers national and global weather, water, climate and space weather guidance, forecasts, warnings and analyses to its Partners and External User Communities...
(US), the European Centre for Medium-Range Weather Forecasts
European Centre for Medium-Range Weather Forecasts
The European Centre for Medium-Range Weather Forecasts is an independent intergovernmental organisation supported by 19 European Member States and 15 Co-operating States...
(ECMWF), the United Kingdom Met Office
Met Office
The Met Office , is the United Kingdom's national weather service, and a trading fund of the Department for Business, Innovation and Skills...
, Meteo France, Environment Canada
Environment Canada
Environment Canada , legally incorporated as the Department of the Environment under the Department of the Environment Act Environment Canada (EC) (French: Environnement Canada), legally incorporated as the Department of the Environment under the Department of the Environment Act Environment...
, the Japanese Meteorological Agency, the Bureau of Meteorology
Bureau of Meteorology
The Bureau of Meteorology is an Executive Agency of the Australian Government responsible for providing weather services to Australia and surrounding areas. It was established in 1906 under the Meteorology Act, and brought together the state meteorological services that existed before then...
(Australia), the China Meteorological Administration
China Meteorological Administration
The China Meteorological Administration , headquartered in Beijing, is the national weather service for the People's Republic of China.-History:...
, the Korea Meteorological Administration
Korea Meteorological Administration
The Korea Meteorological Administration is the National Meteorological service for Korea. The service started in 1904 joining the WMO in 1956. Numerical Weather Prediction is performed using the Unified Model software suite.-External links:* * *...
, and CPTEC (Brazil). Experimental ensemble forecasts are made at a number of universities, such as the University of Washington, and ensemble forecasts in the US are also generated by the US Navy and Air Force. There are various ways of viewing the data such as spaghetti plots, ensemble means or Postage Stamps where a number of different results from the models run can be compared.
History
As proposed by Edward Lorenz in 1963, it is impossible for long-range forecasts—those made more than two weeks in advance—to predict the state of the atmosphere with any degree of skillForecast skill
Skill in forecasting is a scaled representation of forecast error that relates the forecast accuracy of a particular forecast model to some reference model....
, owing to the chaotic nature
Chaos theory
Chaos theory is a field of study in mathematics, with applications in several disciplines including physics, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions, an effect which is popularly referred to as the...
of the fluid dynamics
Fluid dynamics
In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...
equations involved. Furthermore, existing observation networks have limited spatial and temporal resolution (for example, over large bodies of water such as the Pacific Ocean), which introduces uncertainty into the true initial state of the atmosphere. While a set of equations, known as the Liouville equations
Liouville's theorem (Hamiltonian)
In physics, Liouville's theorem, named after the French mathematician Joseph Liouville, is a key theorem in classical statistical and Hamiltonian mechanics...
, exists to determine the initial uncertainty in the model initialization, the equations are too complex to run in real-time, even with the use of supercomputers. These uncertainties limit forecast model accuracy to about six days into the future.
Edward Epstein
Edward Epstein (meteorologist)
Edward Epstein was an American meteorologist who pioneered the use of statistical methods in weather forecasting and the development of ensemble forecasting techniques.During the 1960s he was professor of meteorology at the University of Michigan...
recognized in 1969 that the atmosphere could not be completely described with a single forecast run due to inherent uncertainty, and proposed a stochastic
Stochastic process
In probability theory, a stochastic process , or sometimes random process, is the counterpart to a deterministic process...
dynamic model that produced means
Arithmetic mean
In mathematics and statistics, the arithmetic mean, often referred to as simply the mean or average when the context is clear, is a method to derive the central tendency of a sample space...
and variance
Variance
In probability theory and statistics, the variance is a measure of how far a set of numbers is spread out. It is one of several descriptors of a probability distribution, describing how far the numbers lie from the mean . In particular, the variance is one of the moments of a distribution...
s for the state of the atmosphere. Although these Monte Carlo simulations
Monte Carlo method
Monte Carlo methods are a class of computational algorithms that rely on repeated random sampling to compute their results. Monte Carlo methods are often used in computer simulations of physical and mathematical systems...
showed skill, in 1974 Cecil Leith revealed that they produced adequate forecasts only when the ensemble probability distribution
Probability distribution
In probability theory, a probability mass, probability density, or probability distribution is a function that describes the probability of a random variable taking certain values....
was a representative sample of the probability distribution in the atmosphere. It was not until 1992 that ensemble forecasts began being prepared by the European Centre for Medium-Range Weather Forecasts
European Centre for Medium-Range Weather Forecasts
The European Centre for Medium-Range Weather Forecasts is an independent intergovernmental organisation supported by 19 European Member States and 15 Co-operating States...
and the National Centers for Environmental Prediction
National Centers for Environmental Prediction
The United States National Centers for Environmental Prediction delivers national and global weather, water, climate and space weather guidance, forecasts, warnings and analyses to its Partners and External User Communities...
. The ECMWF model, the Ensemble Prediction System, uses singular vectors
Singular value decomposition
In linear algebra, the singular value decomposition is a factorization of a real or complex matrix, with many useful applications in signal processing and statistics....
to simulate the initial probability density
Probability density function
In probability theory, a probability density function , or density of a continuous random variable is a function that describes the relative likelihood for this random variable to occur at a given point. The probability for the random variable to fall within a particular region is given by the...
, while the NCEP ensemble, the Global Ensemble Forecasting System, uses a technique known as vector breeding.
Variations
When many different forecast models are used to try to generate a forecast, the approach is termed multi-model ensemble forecasting. This method of forecasting has been shown to improve forecasts when compared to a single model-based approach. When the models within a multi-model ensemble are adjusted for their various biases, this process is known as "superensemble forecasting". This type of a forecast significantly reduces errors in model output.Methods of accounting for uncertainty
Stochastic or "ensemble" forecasting is used to account for uncertainty. It involves multiple forecasts created with an individual forecast model by using different physical parametrizationsParametrization (climate)
Parameterization in a weather or climate model within numerical weather prediction refers to the method of replacing processes that are too small-scale or complex to be physically represented in the model by a simplified process. This can be contrasted with other processes—e.g., large-scale flow of...
or varying initial conditions. The ensemble forecast is usually evaluated in terms of an average of the individual forecasts concerning one forecast variable, as well as the degree of agreement between various forecasts within the ensemble system, as represented by their overall spread. Ensemble spread is diagnosed through tools such as spaghetti diagrams, which show the dispersion of one quantity on prognostic charts for specific time steps in the future. Another tool where ensemble spread is used is a meteogram
Meteogram
A meteogram is a time cross-section that produces and uses data for a specific weather station on the ground. It can display past weather conditions up to the current time or forecast conditions from the current time out into the future...
, which shows the dispersion in the forecast of one quantity for one specific location. It is common for the ensemble spread to be too small to incorporate the solution which verifies, which can lead to a misdiagnosis of model uncertainty; this problem becomes particularly severe for forecasts of the weather about 10 days in advance.
Probability assessment
When ensemble spread is small and the forecast solutions are consistent within multiple model runs, forecasters perceive more confidence in the ensemble mean, and the forecast in general. A spread-skill relationship sometimes exists, as spread-error correlations are normally less than 0.6. The relationship between ensemble spread and skillForecast skill
Skill in forecasting is a scaled representation of forecast error that relates the forecast accuracy of a particular forecast model to some reference model....
varies substantially depending on such factors as the forecast model and the region for which the forecast is made.
Ideally, the relative frequency of events from the ensemble could be used directly to estimate the probability of a given weather event. For example, if 30 of 50 members indicated greater than 1 cm rainfall during the next 24 h, the probability of exceeding 1 cm could be estimated to be 60%. The forecast would be considered reliable if, considering all the situations in the past when a 60% probability was forecast, on 60% of those occasions did the rainfall actually exceed 1 cm. This is known as reliability or calibration. In practice, the probabilities generated from operational weather ensemble forecasts are not highly reliable, though with a set of past forecasts (reforecasts or hindcasts) and observations, the probability estimates from the ensemble can be adjusted to ensure greater reliability. Another desirable property of ensemble forecasts is sharpness. Provided that the ensemble is reliable, the more an ensemble forecast deviates from the climatological event frequency and issues 0% or 100% forecasts of an event, the more useful the forecast will be. However, sharp forecasts that are unaccompanied by high reliability will generally not be useful. Forecasts at long leads will inevitably not be particularly sharp, for the inevitable (albeit usually small) errors in the initial condition will grow with increasing forecast lead until the expected difference between two model states is as large as the difference between two random states from the forecast model's climatology.
Research
The Observing System Research and Predictability Experiment (THORPEX) is a 10-year international research and development programme to accelerate improvements in the accuracy of one-day to two-week high impact weather forecastsfor the benefit of society, the economy and the environment.
THORPEX establishes an organizational framework that addresses weather research and forecast problems whose solutions will be accelerated through international collaboration among academic institutions, operational forecast centres and users of forecast products.
TIGGE, the THORPEX Interactive Grand Global Ensemble, is a key component of THORPEX: a World Weather Research Programme to accelerate the improvements in the accuracy of 1-day to 2 week high-impact weather forecasts for the benefit of humanity. Centralized archives of ensemble model forecast data, from many international centers, are used to enable extensive data sharing and research. The designated TIGGE archive centers include the Chinese Meteorological Administration (CMA), The European Center for Medium-Range Weather Forecasts (ECMWF), and The National Center for Atmospheric Research (NCAR). Scientific data requirements and archive planning solidified in late 2005, and archive collection began in October 2006.
The Unidata LDM software package is used to transport the ensemble model data from the providers to the archive centers. Currently, the output from the ECMWF, UK Met Office (UKMO), CMA, Japan Meteorological Agency (JMA), National Centers for Environmental Prediction (NCEP-USA), Meteorological Service of Canada (CMC), Bureau of Meteorology Australia (BOM), Centro de Previsao Tempo e Estudos Climaticos Brazil (CPTEC), Korea Meteorological Administration (KMA), and MeteoFrance (MF) global models, totaling 440 GB/day, is moved at up to 30 GB/hour to NCAR (Realtime Statistics). By requirement the parameter fields, atmospheric levels, and physical units are consistent across all data from the providers and encoded in WMO GRIB-2 format. In contrast, each provider may submit their model output in a resolution they choose.
TIGGE data are available to the public for non-commercial research, with a 48-hour delay after forecast initialization time. At NCAR, users can discover data through the TIGGE portal and select parameters, grid resolution, and spatial subsets for the most current two-week period. The most current two-week period of TIGGE data are also available for direct download in the form of forecast files through the RDA near realtime 2-week TIGGE archive. Long term TIGGE data archives are available through the RDA full TIGGE archive. Forecast files are organized by level type (single level, pressure level, potential vorticity level, and potential temperature level), and forecast time-step for a specified model. All ensemble members are included in each forecast file. At ECMWF, users can discover and download data through a web interface linked to the Meteorological Archival and Retrieval System (MARS). CMA offers an additional option for CMA TIGGE data access. Each center will offer fast access to terabytes of data kept online and delayed access to the long term archives preserved in their archive systems.
The key objectives of TIGGE
- An enhanced collaboration on development of ensemble prediction, internationally and between operational centres and universities,
- New methods of combining ensembles from different sources and of correcting for systematic errors (biases, spread over-/under-estimation),
- A deeper understanding of the contribution of observation, initial and model uncertainties to forecast error,
- A deeper understanding of the feasibility of interactive ensemble system responding dynamically to changing uncertainty (including use for adaptive observing, variable ensemble size, on-demand regional ensembles) and exploiting new technology for grid computing and high-speed data transfer,
- Test concepts of a TIGGE Prediction Centre to produce ensemble-based predictions of high-impact weather, wherever it occurs, on all predictable time ranges,
- The development of a prototype future Global Interactive Forecasting System.
See also
- Chaos theoryChaos theoryChaos theory is a field of study in mathematics, with applications in several disciplines including physics, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions, an effect which is popularly referred to as the...
- Ensemble Kalman filterEnsemble Kalman filterThe ensemble Kalman filter is a recursive filter suitable for problems with a large number of variables, such as discretizations of partial differential equations in geophysical models...
- Ensemble (fluid mechanics)Ensemble (fluid mechanics)In fluid mechanics, an ensemble is an imaginary collection of notionally identical experiments.Each member of the ensemble will have nominally identical boundary conditions and fluid properties...
- ForecastingForecastingForecasting is the process of making statements about events whose actual outcomes have not yet been observed. A commonplace example might be estimation for some variable of interest at some specified future date. Prediction is a similar, but more general term...
- Probabilistic forecastingProbabilistic forecastingProbabilistic forecasting summarises what is known, or opinions about, future events. In contrast to a single-valued forecasts , probabilistic forecasts assign a probability to each of a number of different outcomes,...