The new NOAA operational global sea surface temperature (SST) analysis is described. The analyses use 7 days of in situ (ship and buoy) and satellite SST. These analyses are produced weekly and daily using optimum interpolation (OI) on a 1° grid. The OI technique requires the specification of data and analysis error statistics. These statistics are derived and show that the SST rms data errors from ships are almost twice as large as the data errors from buoys or satellites. In addition, the average e-folding spatial error scales have been found to be 850 km in the zonal direction and 615 km in the meridional direction. The analysis also includes a preliminary step that corrects any satellite biases relative to the in situ data using Poisson's equation. The importance of this correction is demonstrated using recent data following the 1991 eruptions of Mt. Pinatubo. The OI analysis has been computed using the in situ and bias-corrected satellite data for the period 1985 to present.

Improved Global Sea Surface Temperature Analyses Using Optimum Interpolation

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

List of Contributors. Preface. 1. Introduction (I. Jolliffe & D. Stephenson). 2. Basic Concepts (J. Potts). 3. Binary Events (I. Mason). 4. Categorical Events (R. Livezey). 5. Continuous Variables (M. Deque). 6. Verification of Spatial Fields (W. Drosdowsky & H. Zhang). 7. Probability and Ensemble Forecasts (Z. Toth, et al.). 8. Economic Value and Skill (D. Richardson). 9. Forecast Verification: Past, Present and Future (D. Stephenson & I. Jolliffe). Glossary. References. Author Index. Subject Index.

Forecast verification: a practitioner's guide in atmospheric science

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

Atmospheric Modeling, Data Assimilation, and Predictability

The breeding method has been used to generate perturbations for ensemble forecasting at the National Centers for Environmental Prediction (formerly known as the National Meteorological Center) since December 1992. At that time a single breeding cycle with a pair of bred forecasts was implemented. In March 1994, the ensemble was expanded to seven independent breeding cycles on the Cray C90 supercomputer, and the forecasts were extended to 16 days. This provides 17 independent global forecasts valid for two weeks every day. For efficient ensemble forecasting, the initial perturbations to the control analysis should adequately sample the space of possible analysis errors. It is shown that the analysis cycle is like a breeding cycle: it acts as a nonlinear perturbation model upon the evolution of the real atmosphere. The perturbation (i.e., the analysis error), carried forward in the first-guess forecasts, is ‘‘scaled down’’ at regular intervals by the use of observations. Because of this, growing errors associated with the evolving state of the atmosphere develop within the analysis cycle and dominate subsequent forecast error growth. The breeding method simulates the development of growing errors in the analysis cycle. A difference field between two nonlinear forecasts is carried forward (and scaled down at regular intervals) upon the evolving atmospheric analysis fields. By construction, the bred vectors are superpositions of the leading local (timedependent) Lyapunov vectors (LLVs) of the atmosphere. An important property is that all random perturbations assume the structure of the leading LLVs after a transient period, which for large-scale atmospheric processes is about 3 days. When several independent breeding cycles are performed, the phases and amplitudes of individual (and regional) leading LLVs are random, which ensures quasi-orthogonality among the global bred vectors from independent breeding cycles. Experimental runs with a 10-member ensemble (five independent breeding cycles) show that the ensemble mean is superior to an optimally smoothed control and to randomly generated ensemble forecasts, and compares favorably with the medium-range double horizontal resolution control. Moreover, a potentially useful relationship between ensemble spread and forecast error is also found both in the spatial and time domain. The improvement in skill of 0.04‐0.11 in pattern anomaly correlation for forecasts at and beyond 7 days, together with the potential for estimation of the skill, indicate that this system is a useful operational forecast tool. The two methods used so far to produce operational ensemble forecasts—that is, breeding and the adjoint (or ‘‘optimal perturbations’’) technique applied at the European Centre for Medium-Range Weather Forecasts—have several significant differences, but they both attempt to estimate the subspace of fast growing perturbations. The bred vectors provide estimates of fastest sustainable growth and thus represent probable growing analysis errors. The optimal perturbations, on the other hand, estimate vectors with fastest transient growth in the future. A practical difference between the two methods for ensemble forecasting is that breeding is simpler and less expensive than the adjoint technique.

Ensemble Forecasting at NCEP and the Breeding Method

Since modern data assimilation (DA) involves the repetitive use of dynamical forecasts, errors in analyses share characteristics of those in short-range forecasts. Initial conditions for an ensemble prediction/forecast system (EPS or EFS) are expected to sample uncertainty in the analysis field. Ensemble forecasts with such initial conditions can therefore (a) be fed back to DA to reduce analysis uncertainty, as well as (b) sample forecast uncertainty related to initial conditions. Optimum performance of both DA and EFS requires a careful choice of initial ensemble perturbations. DA can be improved with an EFS that represents the dynamically conditioned part of forecast error covariance as accurately as possible, while an EFS can be improved by initial perturbations reflecting analysis error variance. Initial perturbation generation schemes that dynamically cycle ensemble perturbations reminiscent to how forecast errors are cycled in DA schemes may offer consistency between DA and EFS, and good performance for both. In this paper, we introduce an EFS based on the initial perturbations that are generated by the Ensemble Transform (ET) and ET with rescaling (ETR) methods to achieve this goal. Both ET and ETR are generalizations of the breeding method (BM). The results from ensemble systems based on BM, ET, ETR and the Ensemble Transform Kalman Filter (ETKF) method are experimentally compared in the context of ensemble forecast performance. Initial perturbations are centred around a 3D-VAR analysis, with a variance equal to that of estimated analysis errors. Of the four methods, the ETR method performed best in most probabilistic scores and in terms of the forecast error explained by the perturbations. All methods display very high time consistency between the analysis and forecast perturbations. It is expected that DA performance can be improved by the use of forecast error covariance from a dynamically cycled ensemble either with a variational DA approach (coupled with an ETR generation scheme), or with an ETKF-type DA scheme.

Initial perturbations based on the ensemble transform (ET) technique in the NCEP global operational forecast system

The potential economic benefit associated with the use of an ensemble of forecasts versus anequivalent or higher-resolution control forecast is discussed. Neither forecast systems are post-processed,except a simple calibration that is applied to make them reliable. A simple decision-making model is used where all potential users of weather forecasts are characterized by the ratio between the cost of their action to preventweather-related damages, and the loss that they incur in case they do not protect their operations. It isshown that the ensemble forecast system can be used by a much wider range of users. Furthermore,for many, and for beyond 4-day lead time for all users, the ensemble provides greater potential economicbenefit than a control forecast, even if the latter is run at higher horizontal resolution. It is argued that theadded benefits derive from 1) the fact that the ensemble provides a more detailed forecast probabilitydistribution, allowing the users to tailor their weather forecast...

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The economic value of ensemble-based weather forecasts

A new version of the Global Ensemble Forecast System (GEFS, v11) is tested and compared with the operational version (v10) in a 2-yr parallel run. The breeding-based scheme with ensemble transformation and rescaling (ETR) used in the operational GEFS is replaced by the ensemble Kalman filter (EnKF) to generate initial ensemble perturbations. The global medium-range forecast model and the Global Forecast System (GFS) analysis used as the initial conditions are upgraded to the GFS 2015 implementation version. The horizontal resolution of GEFS increases from Eulerian T254 (~52 km) for the first 8 days of the forecast and T190 (~70 km) for the second 8 days to semi-Lagrangian T574 (~34 km) and T382 (~52 km), respectively. The sigma pressure hybrid vertical layers increase from 42 to 64 levels. The verification of geopotential height, temperature, and wind fields at selected levels shows that the new GEFS significantly outperforms the operational GEFS up to days 8–10 except for an increased warm bias o...

Performance of the New NCEP Global Ensemble Forecast System in a Parallel Experiment

Ensemble forecasting has been operational at NCEP (formerly the National Meteorological Center) since December 1992. In March 1994, more ensemble forecast members were added. In the new configuration, 17 forecasts with the NCEP global model are run every day, out to 16-day lead time. Beyond the 3 control forecasts (a T126 and a T62 resolution control at 0000 UTC and a T126 control at 1200 UTC), 14 perturbed forecasts are made at the reduced T62 resolution. Global products from the ensemble forecasts are available from NCEP via anonymous FTP. The initial perturbation vectors are derived from seven independent breeding cycles, where the fast-growing nonlinear perturbations grow freely, apart from the periodic rescaling that keeps their magnitude compatible with the estimated uncertainty within the control analysis. The breeding process is an integral part of the extended-range forecasts, and the generation of the initial perturbations for the ensemble is done at no computational cost beyond that of...

A Synoptic Evaluation of the NCEP Ensemble

The initial perturbations used for the operational global ensemble prediction system of the National Centers for Environmental Prediction are generated through the breeding method with a regional rescaling mechanism. Limitations of the system include the use of a climatologically fixed estimate of the analysis error variance and the lack of an orthogonalization in the breeding procedure. The Ensemble Transform Kalman Filter (ETKF) method is a natural extension of the concept of breeding and, as shown byWang and Bishop, can be used to generate ensemble perturbations that can potentially ameliorate these shortcomings. In the present paper, a spherical simplex 10-member ETKF ensemble, using the actual distribution and error characteristics of real-time observations and an innovation-based inflation, is tested and compared with a 5-pair breeding ensemble in an operational environment. The experimental results indicate only minor differences between the performances of the operational breeding and the experimental ETKF ensemble and only minor differences to Wang and Bishop’s earlier comparison studies. As for the ETKF method, the initial perturbation variance is found to respond to temporal changes in the observational network in the North Pacific. In other regions, however, 10 ETKF perturbations do not appear to be enough to distinguish spatial variations in observational network density. As expected, the whitening effect of the ETKF together with the use of the simplex algorithm that centres a set of quasi-orthogonal perturbations around the best analysis field leads to a significantly higher number of degrees of freedom as compared to the use of paired initial perturbations in operations. As a new result, the perturbations generated through the simplex method are also shown to exhibit a very high degree of consistency between initial analysis and short-range forecast perturbations, a feature that can be important in practical applications. Potential additional benefits of the ETKF and Ensemble Transform methods when using more ensemble members and a more appropriate inflation scheme will be explored in follow-up studies.

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Richard Wobus

Papers

Initial perturbations based on the ensemble transform (ET) technique in the NCEP global operational forecast system

The economic value of ensemble-based weather forecasts

Performance of the New NCEP Global Ensemble Forecast System in a Parallel Experiment

A Synoptic Evaluation of the NCEP Ensemble

Ensemble Transform Kalman Filter-based ensemble perturbations in an operational global prediction system at NCEP