Abstract

Although the development of seamless prediction systems is becoming increasingly common, there is still confusion regarding the relevance of information from initial-value forecasts for assessing the trustworthiness of the climate system’s response to forcing. A simple system that mimics the real climate system through its regime structure is used to illustrate this potential relevance. The more complex version of this model defines “reality” and a simplified version of the system represents the “model.” The model’s response to forcing is profoundly incorrect. However, the untrustworthiness of the model’s response to forcing can be deduced from the model’s initial-value unreliability. The nonlinearity of the system is crucial in accounting for this result.

Abstract

Idealized cloud-resolving model (CRM) simulations spanning a large part of the tropical atmosphere are used to evaluate the extent to which deterministic convective parameterizations fail to capture the statistical fluctuations in deep-convective forcing, and to provide probability distribution functions that may be used in stochastic parameterization schemes for global weather and climate models. A coarse-graining methodology is employed to deduce an effective convective warming rate appropriate to the grid scale of a forecast model, and a convective parameterization scheme is used to bin these computed tendencies into different ranges of convective forcing strength. The dependence of the probability distribution functions for the coarse-grained temperature tendency on parameterized tendency is then examined.

An aquaplanet simulation using a climate model, configured with similar horizontal resolution to that of the coarse-grained CRM fields, was used to compare temperature tendency variation (less the effect of advection and radiation) with that deduced as an effective forcing function from the CRM. The coarse-grained temperature tendency of the CRM is found to have a substantially broader probability distribution function than the equivalent quantity in the climate model.

The CRM-based probability distribution functions of precipitation rate and convective warming are related to the statistical mechanics theory of Craig and Cohen and the “stochastic physics” scheme of Buizza et al. It is found that the standard deviation of the coarse-grained effective convective warming is an approximately linear function of its mean, thereby providing some support for the Buizza et al. scheme, used operationally by ECMWF.

Abstract

Because of the inherent uncertainties in the computational representation of climate and because of unforced chaotic climate variability, it is argued that climate change projections should be expressed in probabilistic form. In this paper, 17 Coupled Model Intercomparison Project second-phase experiments sharing the same gradual increase in atmospheric CO₂ are treated as a probabilistic multimodel ensemble projection of future climate. Tools commonly used for evaluation of probabilistic weather and seasonal forecasts are applied to this climate change ensemble. The probabilities of some temperature- and precipitation-related events defined for 20-yr seasonal means of climate are first studied. A cross-verification exercise is then used to obtain an upper estimate of the quality of these probability forecasts in terms of Brier skill scores, reliability diagrams, and potential economic value. Skill and value estimates are consistently higher for temperature-related events (e.g., will the 20-yr period around the doubling of CO₂ be at least 1°C warmer than the present?) than for precipitation-related events (e.g., will the mean precipitation decrease by 10% or more?). For large enough CO₂ forcing, however, probabilistic projections of precipitation-related events also exhibit substantial potential economic value for a range of cost–loss ratios. The treatment of climate change information in a probabilistic rather than deterministic manner (e.g., using the ensemble consensus forecast) can greatly enhance its potential value.

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 there are typically at least 35 independent singular vectors, which quadruple in amplitude over this timescale. Qualitatively, the distribution of singular vectors can be associated with a simple diagnostic of baroclinic instability from the basic-state flow. However, this relationship is not quantitatively reliable, as, for example, the chosen diagnostic takes no account of the horizontal or time-varying structure of the basic-state flow.

Three basic types of singular vector are identified The most important and most frequent is located in mid latitudes. At initial time, the singular vector is localized in the horizontal, with most amplitude in the lower troposphere. Energy growth can be interpreted qualitatively in terms of wave pseudomomentum propagation into the jet, resulting in peak amplitudes in the upper troposphere at optimization time. During evolution the dominant horizontal wavenumber of the singular vector decreases. Singular vector growth is therefore fundamentally nonmodal. Singular vectors 1ocalized first in the tropical upper troposphere. and second with equivalent barotropic structure in the high-latitude troposhpere, are also identified.

Abstract

Over the past few years, quantum computers and quantum algorithms have attracted considerable interest and attention from numerous scientific disciplines. In this article, we aim to provide a nontechnical yet informative introduction to key aspects of quantum computing. We discuss whether quantum computers one day might become useful tools for numerical weather and climate prediction. Using a recently developed quantum algorithm for solving nonlinear differential equations, we integrate a simple nonlinear model. In addition to considering the advantages that quantum computers have to offer, we shall also discuss the challenges one faces when trying to use quantum computers for real-world problems involving “big data,” such as weather prediction.

Abstract

The interannual variability of rainfall over the Indian subcontinent, the African Sahel, and the Nordeste region of Brazil have been evaluated in 32 models for the period 1979–88 as part of the Atmospheric Model Intercomparison Project (AMIP). The interannual variations of Nordeste rainfall are the most readily captured, owing to the intimate link with Pacific and Atlantic sea surface temperatures. The precipitation variations over India and the Sahel are less well simulated. Additionally, an Indian monsoon wind shear index was calculated for each model. Evaluation of the interannual variability of a wind shear index over the summer monsoon region indicates that the models exhibit greater fidelity in capturing the large-scale dynamic fluctuations than the regional-scale rainfall variations. A rainfall/SST teleconnection quality control was used to objectively stratify model performance. Skill scores improved for those models that qualitatively simulated the observed rainfall/El Niño- Southern Oscillation SST correlation pattern. This subset of models also had a rainfall climatology that was in better agreement with observations, indicating a link between systematic model error and the ability to simulate interannual variations.

A suite of six European Centre for Medium-Range Weather Forecasts (ECMWF) AMIP runs (differing only in their initial conditions) have also been examined. As observed, all-India rainfall was enhanced in 1988 relative to 1987 in each of these realizations. All-India rainfall variability during other years showed little or no predictability, possibly due to internal chaotic dynamics associated with intraseasonal monsoon fluctuations and/or unpredictable land surface process interactions. The interannual variations of Nordeste rainfall were best represented. The State University of New York at Albany/National Center for Atmospheric Research Genesis model was run in five initial condition realizations. In this model, the Nordeste rainfall variability was also best reproduced. However, for all regions the skill was less than that of the ECMWF model.

The relationships of the all-India and Sahel rainfall/SST teleconnections with horizontal resolution, convection scheme closure, and numerics have been evaluated. Models with resolution ≥ T42 performed more poorly than lower-resolution models. The higher resolution models were predominantly spectral. At low resolution, spectral versus gridpoint numerics performed with nearly equal verisimilitude. At low resolution, moisture convergence closure was slightly more preferable than other convective closure techniques. At high resolution, the models that used moisture convergence closure performed very poorly, suggesting that moisture convergence may be problematic for models with horizontal resolution ≥ T42.

Abstract

During the winter of 1988/89, a real-time experimental scheme to predict skill of the ECMWF operational forecast was devised. The scheme was based on statistical relations between skill scores (the predictands) and a number of predictors including consistency between consecutive forecasts, amplitude of very short-range forecast errors, and indices of large-scale regime transitions. The results of the experiment are assessed with particular attention to a period with large variations in the skill of the operational forecast.

Abstract

Two ensembles of 90-day forecasts for 1982–83 have been made with the UK Meteorological Office 11-layer atmospheric general circulation model. Each ensemble comprised three integrations initialized one day apart, using analyses from December 1982. The first ensemble used observed SSTs and the second used climatological SSTs. Our objectives were to compare the skill of the two ensembles and to compare the results with a longer climate sensitivity experiment.

The skill of the forecasts for 10-, 30- and 90-day means was assessed using root-mean-square wind errors at 200 mb. In the tropics, the skill was improved with observed SSTs on all time scales. In the extratropics, the skill was improved on the 30-day time scale except at the initial stages of the forecasts, and the skill was also improved for 90-day means. On the 10-day time scale, however, the improvement was not consistent, and there were periods in which the errors were larger with observed SSTs. The response of the model to the observed SSTs was found to be similar to that of a 540-day perpetual January integration with the winter mean SST anomaly for 1982–83.

Abstract

Using 10-day forecast 500 mb height data from the last 7 yr, the potential to predict the skill of numerical weather forecasts is discussed. Four possible predictor sets are described. The first, giving the consistency between adjacent forecasts, is apparently more skillful if the anomaly correlation coefficient, rather than RMS difference, is used as measure of forecast spread and forecast skill. It is concluded that much of this enhanced skill results from the dependence of the anomaly correlation coefficient on the magnitude of the forecast anomaly. It is noted that the spread between “today's” and “yesterday's” forecast is a more reliable estimate of the skill of yesterday's forecast than today's, and the implications of this on lagged-average ensemble forecasts are discussed. The impact of temporal filtering of the data in spread/skill correlations are also described.

The second predictor set is derived from a regression analysis between RMS error skill scores and EOF coefficients of the forecast and/or initial 500 mb heights. The predictors themselves are large-scale anomaly patterns, some of which, towards the end of the forecast period, resemble low-frequency teleconnection patterns of the atmosphere. It is shown that forecast EOF coefficients are more skilful predictors than EOF coefficients of the initial conditions, and that when both sets of coefficients are used in the regression there is a danger of overfitting. The dependence of these patterns on the truncation of the EOF expansion and of temporal filtering is discussed. In particular, it is shown that when a severe EOF truncation is made, some of the forecast flow anomaly patterns become less geographically localized, indicating poorer predictive skill.

The third predictor is defined as the RMS skill of the day-1 forecast. Both upstream and local correlations are studied. It is shown that with day-1 forecast error leading day-3 RMS error by up to 3 days, there appears to be a propagating signal, in addition to a quasi-stationary one. In general, the latter appears to be dominant. The fourth predictor is defined as the RMS difference between the forecast 500 mb height, and the initial 500 mb height. Use of this latter predictor was motivated by diagnostic studies showing relationships between interannual variability of forecast scores and interannual variability of persistence errors. These studies are partly described here. It is shown that the use of forecast persistence as a predictor gives partial skill, at least towards the end of the forecast period.

The skill of the predictors are tested, and the regression coefficients derived, on data from six winters, for both regional and hemispheric skill scores. As an independent test, the predictors are also applied separately to the seventh winter period 1986/87. It is concluded that some aspects of the low-frequency component of forecast skill variability can be satisfactorily predicted, though significant high frequency variability remains unpredicted.

In discussing the physical mechanisms that underlie the use of these predictors, three important components of forecast skill variability are discussed: the quality of the initial analysis, the intrinsic instability of the flow, and the role of model systematic errors.

It is shown that results from the EOF predictor for the European region towards the end of the forecast period are strongly influenced by model systematic error. On the other hand, over the Pacific/North American region, growth of errors on flows with varying barotropic stability characteristics are an important component of medium-range forecast variability. This is discussed using a barotropic model with basic states defined from the results of the regression analyses for various regions. At shorter range it is suggested that growth of errors by baroclinic processes is probably dominant.