This comprehensive text and reference work on numerical weather prediction, first published in 2002, covers not only methods for numerical modeling, but also the important related areas of data assimilation and predictability. It incorporates all aspects of environmental computer modeling including an historical overview of the subject, equations of motion and their approximations, a modern and clear description of numerical methods, and the determination of initial conditions using weather observations (an important science known as data assimilation). Finally, this book provides a clear discussion of the problems of predictability and chaos in dynamical systems and how they can be applied to atmospheric and oceanic systems. Professors and students in meteorology, atmospheric science, oceanography, hydrology and environmental science will find much to interest them in this book, which can also form the basis of one or more graduate-level courses.

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Atmospheric Modeling, Data Assimilation and Predictability

A theory for estimating the probability distribution of the state of a model given a set of observations exists. This nonlinear filtering theory unifies the data assimilation and ensemble generation problem that have been key foci of prediction and predictability research for numerical weather and ocean prediction applications. A new algorithm, referred to as an ensemble adjustment Kalman filter, and the more traditional implementation of the ensemble Kalman filter in which “perturbed observations” are used, are derived as Monte Carlo approximations to the nonlinear filter. Both ensemble Kalman filter methods produce assimilations with small ensemble mean errors while providing reasonable measures of uncertainty in the assimilated variables. The ensemble methods can assimilate observations with a nonlinear relation to model state variables and can also use observations to estimate the value of imprecisely known model parameters. These ensemble filter methods are shown to have significant advantag...

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An Ensemble Adjustment Kalman Filter for Data Assimilation

Ensembles used for probabilistic weather forecasting often exhibit a spread-error correlation, but they tend to be underdispersive. This paper proposes a statistical method for postprocessing ensembles based on Bayesian model averaging (BMA), which is a standard method for combining predictive distributions from different sources. The BMA predictive probability density function (PDF) of any quantity of interest is a weighted average of PDFs centered on the individual bias-corrected forecasts, where the weights are equal to posterior probabilities of the models generating the forecasts and reflect the models’ relative contributions to predictive skill over the training period. The BMA weights can be used to assess the usefulness of ensemble members, and this can be used as a basis for selecting ensemble members; this can be useful given the cost of running large ensembles. The BMA PDF can be represented as an unweighted ensemble of any desired size, by simulating from the BMA predictive distribution. The BMA predictive variance can be decomposed into two components, one corresponding to the between-forecast variability, and the second to the within-forecast variability. Predictive PDFs or intervals based solely on the ensemble spread incorporate the first component but not the second. Thus BMA provides a theoretical explanation of the tendency of ensembles to exhibit a spread-error correlation but yet be underdispersive. The method was applied to 48-h forecasts of surface temperature in the Pacific Northwest in January– June 2000 using the University of Washington fifth-generation Pennsylvania State University–NCAR Mesoscale Model (MM5) ensemble. The predictive PDFs were much better calibrated than the raw ensemble, and the BMA forecasts were sharp in that 90% BMA prediction intervals were 66% shorter on average than those produced by sample climatology. As a by-product, BMA yields a deterministic point forecast, and this had root-mean-square errors 7% lower than the best of the ensemble members and 8% lower than the ensemble mean. Similar results were obtained for forecasts of sea level pressure. Simulation experiments show that BMA performs reasonably well when the underlying ensemble is calibrated, or even overdispersed.

https://www.stat.washington.edu/raftery/Research/PDF/fadoua2005.pdf

Using Bayesian Model Averaging to Calibrate Forecast Ensembles

(2005). Atmospheric Modeling, Data Assimilation, and Predictability. Technometrics: Vol. 47, No. 4, pp. 521-521.

Atmospheric Modeling, Data Assimilation, and Predictability

The European Centre for Medium-Range Weather Forecasts (ECMWF) Ensemble Prediction System (EPS) is described. In addition to an unperturbed (control) forecast, each ensemble comprises 32 10-day forecasts starting from initial conditions in which dynamically defined perturbations have been added to the operational analysis. The perturbations are constructed from singular vectors of a time-evolution operator linearized around the short-range-forecast trajectory. These singular vectors approximately determine the most unstable phase-space directions in the early part of the forecast period, and are estimated using a forward and adjoint linear version of the ECMWF numerical weather-prediction model. An appropriate norm is chosen, and relationships between the structures of these singular vectors at initial time and patterns showing the sensitivity of short-range forecast error to changes in the analysis are discussed. A methodology to perform a phase-space rotation of the singular vectors is described, which generates hemispheric-wide perturbations and renormalizes them according to analysis-error estimates from the data-assimilation system.

The validation of the ensembles is given firstly in terms of scatter diagrams and contingency tables of ensemble spread and control-forecast skill. The contingency tables are compared with those from a perfect-model ensemble system; no significant differences are found in some cases. Brier scores for the probability of European flow clusters are presented, which indicate predictive skill up to forecast-day 8 with respect to climatological probabilities. The dependence of these scores on flow-dependent model errors is also discussed. Finally, ensemble-member skill-score distributions are presented, which confirm the overall satisfactory performance of the EPS, particularly in summer and autumn 1993. In winter, cases of poor performance over Europe were associated with the occurrence of a split westerly flow with a blocking high and/or a cut-off low in the verifying analysis.

Two cases are studied in detail, one having large ensemble dispersion, the other corresponding to a more predictable situation. The case studies are used to illustrate the range of ensemble products routinely disseminated to ECMWF Member States. These products include clusters of flow types, and probability fields of weather elements.

The ECMWF Ensemble Prediction System: Methodology and validation

On 7 December 1992 NMC began operational ensemble prediction. The ensemble configuration provides 14 independent forecasts every day, verifying on days 1 through 10. The ensemble members are generated through a combination of time lagging [Lagged-Average Forecasting] and a new method, Breeding of Growing Modes (Toth and Kalnay). In adopting the ensemble approach, NMC explicitly recognizes that forecasts are stochastic, not deterministic, in nature. There is no single solution, only an array of possibilities, and forecast ensembles provide a rational basis for assessing the range and likelihood of alternative scenarios. Given the near saturation of computer resources at NMC, implementation of ensemble prediction required a trade-off between model resolution and multiple runs. Before 7 December 1992, NMC was producing a single global forecast through 10 days with the highest-resolution (T126) version possible of its medium-range forecast model. Now, based an experiments that showed no adverse impac...

Operational Ensemble Prediction at the National Meteorological Center: Practical Aspects

Numerical forecasts from a pilot program on short-range ensemble forecasting at the National Centers for Environmental Prediction are examined. The ensemble consists of 10 forecasts made using the 80-km Eta Model and 5 forecasts from the regional spectral model. Results indicate that the accuracy of the ensemble mean is comparable to that from the 29-km Meso Eta Model for both mandatory level data and the 36-h forecast cyclone position. Calculations of spread indicate that at 36 and 48 h the spread from initial conditions created using the breeding of growing modes technique is larger than the spread from initial conditions created using different analyses. However, the accuracy of the forecast cyclone position from these two initialization techniques is nearly identical. Results further indicate that using two different numerical models assists in increasing the ensemble spread significantly. There is little correlation between the spread in the ensemble members and the accuracy of the ensemble mean for the prediction of cyclone location. Since information on forecast uncertainty is needed in many applications, and is one of the reasons to use an ensemble approach, the lack of a correlation between spread and forecast uncertainty presents a challenge to the production of short-range ensemble forecasts. Even though the ensemble dispersion is not found to be an indication of forecast uncertainty, significant spread can occur within the forecasts over a relatively short time period. Examples are shown to illustrate how small uncertainties in the model initial conditions can lead to large differences in numerical forecasts from an identical numerical model.

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Using Ensembles for Short-Range Forecasting

Early results are presented of an experimental program in Dynamical Extended Range Forecasting at the National Meteorological Center. The primary objective of this program is to assess the feasibility of extending operational numerical weather prediction beyond the medium range to the monthly outlook problem. Additionally, the extended integrations provide greater insight into systematic errors and climate drift and thereby feedback to model development. In this paper the principal focus is upon assessment of a contiguous set of 108 thirty-day integrations generated with the then operational Medium Range Forecast model from initial conditions 24 hours apart between 14 December 1986 and 31 March 1987. Results indicate some serious model deficiencies such as the tendency for zonalization, i.e., systematically stronger midlatitude zonal flow than observed, and a stratospheric cold bias, which continues to grow through the 30--day integrations. In the 1–30 day mean Northern Hemisphere 500 mb height f...

Dynamical Extended Range Forecasting (DERF) at the National Meteorological Center

This paper addresses that aspect of predictability which appears related to scale interaction processes in blocking. The basic approach consists of synoptic analysis and quasi-geostrophic diagnosis of the dynamical processes in the real versus forecast model atmosphere. Time–longitude plots of a blocking index, together with sequences of 500 mb height charts, are used to show the temporal and spatial relationships of circulation systems of three distinct wavebands; planetary, medium and short scale, defined as total wavenumbers 0–6, 7–12, and 13–30, respectively. The relevant quasi-geostrophic concepts and equations are formulated to permit explicit evaluation of the relative importance of barotropic versus baroclinic mechanisms and the contributions to each of scale interactive and non- (or self-) interactive processes. The case discussed here is the Atlantic/European blocking of January 1987, particularly the initial stage of development (3–12 January), and was drawn from the recent National Me...

M. Steven Tracton

Papers

Operational Ensemble Prediction at the National Meteorological Center: Practical Aspects

Using Ensembles for Short-Range Forecasting

Dynamical Extended Range Forecasting (DERF) at the National Meteorological Center

Predictability and Its Relationship to Scale Interaction Processes in Blocking

Application of the NCEP/EMC Short Range Ensemble Forecast System (SREF) to Predicting Extreme Precipitation Events