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Fedor Mesinger, Miodrag Rančić, and R. James Purser

The astonishing development of computer technology since the mid-20th century has been accompanied by a corresponding proliferation in the numerical methods that have been developed to improve the simulation of atmospheric flows. This article reviews some of the numerical developments concern the ongoing improvements of weather forecasting and climate simulation models. Early computers were single-processor machines with severely limited memory capacity and computational speed, requiring simplified representations of the atmospheric equations and low resolution. As the hardware evolved and memory and speed increased, it became feasible to accommodate more complete representations of the dynamic and physical atmospheric processes. These more faithful representations of the so-called primitive equations included dynamic modes that are not necessarily of meteorological significance, which in turn led to additional computational challenges. Understanding which problems required attention and how they should be addressed was not a straightforward and unique process, and it resulted in the variety of approaches that are summarized in this article. At about the turn of the century, the most dramatic developments in hardware were the inauguration of the era of massively parallel computers, together with the vast increase in the amount of rapidly accessible memory that the new architectures provided. These advances and opportunities have demanded a thorough reassessment of the numerical methods that are most successfully adapted to this new computational environment. This article combines a survey of the important historical landmarks together with a somewhat speculative review of methods that, at the time of writing, seem to hold out the promise of further advancing the art and science of atmospheric numerical modeling.


Stefano Tibaldi and Franco Molteni

The atmospheric circulation in the mid-latitudes of both hemispheres is usually dominated by westerly winds and by planetary-scale and shorter-scale synoptic waves, moving mostly from west to east. A remarkable and frequent exception to this “usual” behavior is atmospheric blocking. Blocking occurs when the usual zonal flow is hindered by the establishment of a large-amplitude, quasi-stationary, high-pressure meridional circulation structure which “blocks” the flow of the westerlies and the progression of the atmospheric waves and disturbances embedded in them. Such blocking structures can have lifetimes varying from a few days to several weeks in the most extreme cases. Their presence can strongly affect the weather of large portions of the mid-latitudes, leading to the establishment of anomalous meteorological conditions. These can take the form of strong precipitation episodes or persistent anticyclonic regimes, leading in turn to floods, extreme cold spells, heat waves, or short-lived droughts. Even air quality can be strongly influenced by the establishment of atmospheric blocking, with episodes of high concentrations of low-level ozone in summer and of particulate matter and other air pollutants in winter, particularly in highly populated urban areas. Atmospheric blocking has the tendency to occur more often in winter and in certain longitudinal quadrants, notably the Euro-Atlantic and the Pacific sectors of the Northern Hemisphere. In the Southern Hemisphere, blocking episodes are generally less frequent, and the longitudinal localization is less pronounced than in the Northern Hemisphere. Blocking has aroused the interest of atmospheric scientists since the middle of the last century, with the pioneering observational works of Berggren, Bolin, Rossby, and Rex, and has become the subject of innumerable observational and theoretical studies. The purpose of such studies was originally to find a commonly accepted structural and phenomenological definition of atmospheric blocking. The investigations went on to study blocking climatology in terms of the geographical distribution of its frequency of occurrence and the associated seasonal and inter-annual variability. Well into the second half of the 20th century, a large number of theoretical dynamic works on blocking formation and maintenance started appearing in the literature. Such theoretical studies explored a wide range of possible dynamic mechanisms, including large-amplitude planetary-scale wave dynamics, including Rossby wave breaking, multiple equilibria circulation regimes, large-scale forcing of anticyclones by synoptic-scale eddies, finite-amplitude non-linear instability theory, and influence of sea surface temperature anomalies, to name but a few. However, to date no unique theoretical model of atmospheric blocking has been formulated that can account for all of its observational characteristics. When numerical, global short- and medium-range weather predictions started being produced operationally, and with the establishment, in the late 1970s and early 1980s, of the European Centre for Medium-Range Weather Forecasts, it quickly became of relevance to assess the capability of numerical models to predict blocking with the correct space-time characteristics (e.g., location, time of onset, life span, and decay). Early studies showed that models had difficulties in correctly representing blocking as well as in connection with their large systematic (mean) errors. Despite enormous improvements in the ability of numerical models to represent atmospheric dynamics, blocking remains a challenge for global weather prediction and climate simulation models. Such modeling deficiencies have negative consequences not only for our ability to represent the observed climate but also for the possibility of producing high-quality seasonal-to-decadal predictions. For such predictions, representing the correct space-time statistics of blocking occurrence is, especially for certain geographical areas, extremely important.