Abstract

Data assimilation combines forecasts from a numerical model with observations. Most of the current data assimilation algorithms consider the model and observation error terms as additive Gaussian noise, specified by their covariance matrices $\mathsf{Q}$ and $\mathsf{R}$ , respectively. These error covariances, and specifically their respective amplitudes, determine the weights given to the background (i.e., the model forecasts) and to the observations in the solution of data assimilation algorithms (i.e., the analysis). Consequently, $\mathsf{Q}$ and $\mathsf{R}$ matrices significantly impact the accuracy of the analysis. This review aims to present and to discuss, with a unified framework, different methods to jointly estimate the $\mathsf{Q}$ and $\mathsf{R}$ matrices using ensemble-based data assimilation techniques. Most of the methods developed to date use the innovations, defined as differences between the observations and the projection of the forecasts onto the observation space. These methods are based on two main statistical criteria: 1) the method of moments, in which the theoretical and empirical moments of the innovations are assumed to be equal, and 2) methods that use the likelihood of the observations, themselves contained in the innovations. The reviewed methods assume that innovations are Gaussian random variables, although extension to other distributions is possible for likelihood-based methods. The methods also show some differences in terms of levels of complexity and applicability to high-dimensional systems. The conclusion of the review discusses the key challenges to further develop estimation methods for $\mathsf{Q}$ and $\mathsf{R}$ . These challenges include taking into account time-varying error covariances, using limited observational coverage, estimating additional deterministic error terms, or accounting for correlated noise.

Abstract

This paper reviews recent research that assesses evidence for the detection of anthropogenic and natural external influences on the climate. Externally driven climate change has been detected by a number of investigators in independent data covering many parts of the climate system, including surface temperature on global and large regional scales, ocean heat content, atmospheric circulation, and variables of the free atmosphere, such as atmospheric temperature and tropopause height. The influence of external forcing is also clearly discernible in reconstructions of hemispheric-scale temperature of the last millennium. These observed climate changes are very unlikely to be due only to natural internal climate variability, and they are consistent with the responses to anthropogenic and natural external forcing of the climate system that are simulated with climate models. The evidence indicates that natural drivers such as solar variability and volcanic activity are at most partially responsible for the large-scale temperature changes observed over the past century, and that a large fraction of the warming over the last 50 yr can be attributed to greenhouse gas increases. Thus, the recent research supports and strengthens the IPCC Third Assessment Report conclusion that “most of the global warming over the past 50 years is likely due to the increase in greenhouse gases.”

Abstract

This paper offers a critical review of the topic of cloud–climate feedbacks and exposes some of the underlying reasons for the inherent lack of understanding of these feedbacks and why progress might be expected on this important climate problem in the coming decade. Although many processes and related parameters come under the influence of clouds, it is argued that atmospheric processes fundamentally govern the cloud feedbacks via the relationship between the atmospheric circulations, cloudiness, and the radiative and latent heating of the atmosphere. It is also shown how perturbations to the atmospheric radiation budget that are induced by cloud changes in response to climate forcing dictate the eventual response of the global-mean hydrological cycle of the climate model to climate forcing. This suggests that cloud feedbacks are likely to control the bulk precipitation efficiency and associated responses of the planet’s hydrological cycle to climate radiative forcings.

The paper provides a brief overview of the effects of clouds on the radiation budget of the earth–atmosphere system and a review of cloud feedbacks as they have been defined in simple systems, one being a system in radiative–convective equilibrium (RCE) and others relating to simple feedback ideas that regulate tropical SSTs. The systems perspective is reviewed as it has served as the basis for most feedback analyses. What emerges is the importance of being clear about the definition of the system. It is shown how different assumptions about the system produce very different conclusions about the magnitude and sign of feedbacks. Much more diligence is called for in terms of defining the system and justifying assumptions. In principle, there is also neither any theoretical basis to justify the system that defines feedbacks in terms of global–time-mean changes in surface temperature nor is there any compelling empirical evidence to do so. The lack of maturity of feedback analysis methods also suggests that progress in understanding climate feedback will require development of alternative methods of analysis.

It has been argued that, in view of the complex nature of the climate system, and the cumbersome problems encountered in diagnosing feedbacks, understanding cloud feedback will be gleaned neither from observations nor proved from simple theoretical argument alone. The blueprint for progress must follow a more arduous path that requires a carefully orchestrated and systematic combination of model and observations. Models provide the tool for diagnosing processes and quantifying feedbacks while observations provide the essential test of the model’s credibility in representing these processes. While GCM climate and NWP models represent the most complete description of all the interactions between the processes that presumably establish the main cloud feedbacks, the weak link in the use of these models lies in the cloud parameterization imbedded in them. Aspects of these parameterizations remain worrisome, containing levels of empiricism and assumptions that are hard to evaluate with current global observations. Clearly observationally based methods for evaluating cloud parameterizations are an important element in the road map to progress.

Although progress in understanding the cloud feedback problem has been slow and confused by past analysis, there are legitimate reasons outlined in the paper that give hope for real progress in the future.

Abstract

A review of the cumulus parameterization problem is presented with an emphasis on its conceptual aspects covering the history of the underlying ideas, major problems existing at present, and possible directions and approaches for future climate models. Since its introduction in the early 1960s, there have been decades of controversies in posing the cumulus parameterization problem. In this paper, it is suggested that confusion between budget and advection considerations is primarily responsible for the controversies. It is also pointed out that the performance of parameterization schemes can be better understood if one is not bound by their authors' justifications. The current trend in posing cumulus parameterization is away from deterministic diagnostic closures, including instantaneous adjustments, toward prognostic or nondeterministic closures, including relaxed and/or triggered adjustments. A number of questions need to be answered, however, for the merit of this trend to be fully utilized.

Major practical and conceptual problems in the conventional approach of cumulus parameterization, which include artificial separations of processes and scales, are then discussed. It is rather obvious that for future climate models the scope of the problem must be drastically expanded from “cumulus parameterization” to “unified cloud parameterization,” or even to “unified model physics.” This is an extremely challenging task, both intellectually and computationally, and the use of multiple approaches is crucial even for a moderate success. “Cloud-resolving convective parameterization” or “superparameterization” is a promising new approach that can develop into a multiscale modeling framework (MMF). It is emphasized that the use of such a framework can unify our currently diversified modeling efforts and make verification of climate models against observations much more constructive than it is now.