Roberto Buizza

The singular-vector structure of the atmospheric global circulation

Abstract The local phase-space instability Of the atmospheric global circulation is Characterized by its (nonmodal) singular vectors. The formalism of singular vector analysis is described. The relations between singular vectors, normal modes, adjoint modes, Lyapunov vectors, perturbations produced by the so-called breeding method, and wave pseudomomentum are outlined. Techniques to estimate the dominant part of the singular spectrum using large-dimensional primitive equation models are discussed. These include the use of forward and adjoint tangent propagators with a Lanczos iterative algorithm. Results are described, based first on statistics of routine calculations made between December 1992 and August 1993, and second on three specific case studies. Results define three dominant geographical areas of instability in the Northern Hemisphere: the two regions of storm track cyclogenesis, and the North African subtropical jet Singular vectors can amplify as much as tenfold over 36 hours, and in winter ther...

A Comparison of the ECMWF, MSC, and NCEP Global Ensemble Prediction Systems

Abstract The present paper summarizes the methodologies used at the European Centre for Medium-Range Weather Forecasts (ECMWF), the Meteorological Service of Canada (MSC), and the National Centers for Environmental Prediction (NCEP) to simulate the effect of initial and model uncertainties in ensemble forecasting. The characteristics of the three systems are compared for a 3-month period between May and July 2002. The main conclusions of the study are the following: the performance of ensemble prediction systems strongly depends on the quality of the data assimilation system used to create the unperturbed (best) initial condition and the numerical model used to generate the forecasts; a successful ensemble prediction system should simulate the effect of both initial and model-related uncertainties on forecast errors; and for all three global systems, the spread of ensemble forecasts is insufficient to systematically capture reality, suggesting that none of them is able to simulate all sources of forecast ...

Singular Vectors, Metrics, and Adaptive Observations

Singular vectors of the linearized equations of motion have been used to study the instability properties of the atmosphere‐ocean system and its related predictability. A third use of these singular vectors is proposed here: as part of a strategy to target adaptive observations to ‘‘sensitive’’ parts of the atmosphere. Such observations could be made using unmanned aircraft, though calculations in this paper are motivated by the upstream component of the Fronts and Atlantic Storm-Track Experiment. Oceanic applications are also discussed. In defining this strategy, it is shown that there is, in principle, no freedom in the choice of inner product or metric for the singular vector calculation. However, the correct metric is dependent on the purpose for making the targeted observations (to study precursor developments or to improve forecast initial conditions). It is argued that for predictability studies, where both the dynamical instability properties of the system and the specification of the operational observing network and associated data assimilation system are important, the appropriate metric will differ from that appropriate to a pure geophysical fluid dynamics (GFD) problem. Based on two different sets of calculations, it is argued that for predictability studies (but not for GFD studies), a first-order approximation to the appropriate metric can be based on perturbation energy. The role of observations in data assimilation procedures (constraining large scales more than small scales) is fundamental in understanding reasons for the requirement for different metrics for the two classes of problems. An index-based tensor approach is used to make explicit the role of the metric. The strategy for using singular vectors to target adaptive observations is discussed in the context of other possible approaches, specifically, based on breeding vectors, potential vorticity diagnosis, and sensitivity vectors. The basic premises underlying the use of breeding and singular vectors are discussed. A comparison of the growth rates of breeding and singular vectors is made using a T21 quasigeostrophic model. Singular vectors and subjective potential vorticity (PV) diagnosis are compared for a particular case study. The areas of sensitivity indicated by the two methods only partially agree. Reasons for disagreement hinge around the fact that subjective PV diagnosis emphasizes Lagrangian advection, whereas singular vector analysis emphasizes wave propagation. For the latter, areas of sensitivity may be associated with regions of weak PV gradient, for example, mid to lower troposphere. Amplification of singular vectors propagating from regions of weak PV gradient to regions of strong PV gradient is discussed in terms of pseudomomentum conservation. Evidence is shown that analysis error may be as large in the lower midtroposphere as in the upper troposphere.

Neural network load forecasting with weather ensemble predictions

In recent years, a large literature has evolved on the use of artificial neural networks (NNs) for electric load forecasting. NNs are particularly appealing because of their ability to model an unspecified non-linear relationship between load and weather variables. Weather forecasts are a key input when the NN is used for forecasting. This study Investigates the use of weather ensemble predictions in the application of NNs to load forecasting for lead times from 1 to 10 days ahead. A weather ensemble prediction consists of multiple scenarios for a weather variable. We use these scenarios to produce multiple scenarios for load. The results show that the average of the load scenarios is a more accurate load forecast than that produced using traditional weather forecasts. We use the load scenarios to estimate the uncertainty in the NN load forecast This compares favourably with estimates based solely on historical load forecast errors.

Wind Power Density Forecasting Using Ensemble Predictions and Time Series Models

Wind power is an increasingly used form of renewable energy. The uncertainty in wind generation is very large due to the inherent variability in wind speed, and this needs to be understood by operators of power systems and wind farms. To assist with the management of this risk, this paper investigates methods for predicting the probability density function of generated wind power from one to ten days ahead at five U.K. wind farm locations. These density forecasts provide a description of the expected future value and the associated uncertainty. We construct density forecasts from weather ensemble predictions, which are a relatively new type of weather forecast generated from atmospheric models. We also consider density forecasting from statistical time series models. The best results for wind power density prediction and point forecasting were produced by an approach that involves calibration and smoothing of the ensemble-based wind power density.

Potential Forecast Skill of Ensemble Prediction and Spread and Skill Distributions of the ECMWF Ensemble Prediction System

Abstract Ensemble forecasting is a feasible method to integrate a deterministic forecast with an estimate of the probability distribution of atmospheric states. At the European Centre for Medium-Range Weather Forecasts (ECMWF), the Ensemble Prediction System (EPS) comprises 32 perturbed and 1 unperturbed nonlinear integrations, at T63 spectral triangular truncation and with 19 vertical levels. The perturbed initial conditions are generated using the most unstable directions growing over a 48-h time period, computed at T42L19 resolution. This work describes the performance of the ECMWF EPS during the first 21 months of daily operation, from 1 May 1994 to 31 January 1996, focusing on the 500-hPa geopotential height fields. First, the EPS is described, and the validation approach followed throughout this work is discussed. In particular, spread and skill distribution functions are introduced to define a more integral validation methodology for ensemble prediction. Then, the potential forecast skill of ensemb...

Using weather ensemble predictions in electricity demand forecasting

Weather forecasts are an important input to many electricity demand forecasting models. This study investigates the use of weather ensemble predictions in electricity demand forecasting for lead times from 1 to 10 days ahead. A weather ensemble prediction consists of 51 scenarios for a weather variable. We use these scenarios to produce 51 scenarios for the weather-related component of electricity demand. The results show that the average of the demand scenarios is a more accurate demand forecast than that produced using traditional weather forecasts. We use the distribution of the demand scenarios to estimate the demand forecast uncertainty. This compares favourably with estimates produced using univariate volatility forecasting methods.

Impact of Ensemble Size on Ensemble Prediction

Abstract The impact of ensemble size on the performance of the European Centre for Medium-Range Weather Forecasts ensemble prediction system (EPS) is analyzed. The skill of ensembles generated using 2, 4, 8, 16, and 32 perturbed ensemble members are compared for a period of 45 days—from 1 October to 15 November 1996. For each ensemble configuration, the skill is compared with the potential skill, measured by randomly choosing one of the 32 ensemble members as verification (idealized ensemble). Results are based on the analyses of the prediction of the 500-hPa geopotential height field. Various measures of performance are applied: skill of the ensemble mean, spread–skill relationship, skill of most accurate ensemble member, Brier score, ranked probability score, relative operating characteristic, and the outlier statistic. The relation between ensemble spread and control error is studied using L2, L8, and L∞ norms to measure distances between ensemble members and the control forecast or the verification. I...

Probabilistic Predictions of Precipitation Using the ECMWF Ensemble Prediction System

The forecast skill of the European Centre for Medium-Range Weather Forecasts Ensemble Prediction System (EPS) in predicting precipitation probabilities is discussed. Four seasons are analyzed in detail using signal detection theory and reliability diagrams to define objective measure of predictive skill. First, the EPS performance during summer 1997 is discussed. Attention is focused on Europe and two European local regions, one centered around the Alps and the other around Ireland. Results indicate that for Europe the EPS can give skillful prediction of low precipitation amounts [i.e., lower than 2 mm (12 h) 21] up to forecast day 6, and of high precipitation amounts [i.e., between 2 and 10 mm (12 h)21] up to day 4. Lower levels of skill are achieved for smaller local areas. Then, the EPS performance during summer 1996 (i.e., prior to the enhancement introduced on 10 December 1996 from 33 to 51 members and to resolution increase from T63 L19 to TL159 L31) and summer 1997 are compared. Results show that the EPS has been remarkably more skillful during summer 1997 than summer 1996, with the gain in predictability up to 3 days for the highest [5 and 10 mm (12 h) 21] amounts of precipitation. Finally, the EPS performance during wintertime is analyzed. Two issues are investigated: the seasonal variability of the forecast skill of the new EPS, and the impact of the system upgrade on the wintertime performance. The comparison of the performance of the new EPS system during winter 1996/97 and during summer 1997 indicates that the EPS is more skillful during winter than during summer, with differences in predictive skill around 3 days for precipitation amounts larger than 2 mm (12 h)21. The comparison of the EPS performance before and after the system upgrade on 10 December 1996 during winter confirms the summer conclusion that the upgraded system is more skillful than the old one.

Sensitivity Analysis of Forecast Errors and the Construction of Optimal Perturbations Using Singular Vectors

Abstract The sensitivity of forecast errors to initial conditions is used to examine the optimality of perturbations constructed from the singular vectors of the tangent propagator of the European Centre for Medium-Range Weather Forecasts model. Sensitivity and pseudo-inverse perturbations based on the 48-h forecast error are computed as explicit linear combinations of singular vectors optimizing total energy over the Northern Hemisphere. It is assumed that these perturbations are close to the optimal perturbation that can be constructed from a linear combination of these singular vectors. Optimality is measured primarily in terms of the medium-range forecast improvement obtained by adding the perturbations a posteriori to the initial conditions. Several issues are addressed in the context of these experiments, including the ability of singular vectors to describe forecast error growth beyond the optimization interval, the number of singular vectors required, and the implications of nonmodal error growth....