Recent advances in Lagrangian atmospheric transport models

I liked this brief review article in Eos of some recent advances in the modeling of chemical transport models. Excerpt below, since the article is behind a pay-wall.

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Lagrangian models (LMs) track the movement of fluid parcels in their moving frame of reference. As such, scientists using LMs are forced, in a way, to imagine themselves moving with the parcel and experiencing the effects of advection, turbulence, and changes in the parcel’s environment.

LMs have advanced in sophistication over recent decades, allowing them to be used increasingly for both scientific and societal purposes. For example, it is common practice now for researchers around the world to apply LMs to examine a wide spectrum of geophysical phenomena. Atmospheric chemists can track intercontinental transport of pollution plumes [Stohl et al., 2002] or airborne radioactivity [Wotawa et al.,2006]. By running LMs backward in time [Flesch et al., 1995; Lin et al., 2003], instrumentalists can establish the source regions of observed atmospheric species with high computational efficiency [Ryall et al., 2001]. Therefore, LMs are being used increasingly to quantify sources and sinks of greenhouse gases by combining simulations with observations in an inverse modeling framework [Trusilova et al., 2010]. Such “top-down”emissions estimation is receiving growing acceptance as an independent tool to test the veracity of emissions inventories and to verify adherence to treaties. 

A recent indication of the tremendous societal importance of LMs was their role in predicting the spread of volcanic ash from the eruption of Eyjafjallajökull volcano inIceland. Figure 1 demonstrates the power ofLMs to accurately track the multiday dispersion of a plume as it eventually transforms into a complicated filamentary structure. The example further demonstrates the great potential of applying LMs in combination with data assimilation and inverse modeling to improve source estimates and the simulation of hazardous plumes.

As Lagrangian modeling increases in complexity and popularity, it is imperative to reexamine the physical foundations and implementation aspects of LMs used today.From this, scientists can build a road map of further steps needed to move Lagrangian modeling forward and to ensure its successful application in the future.

As opposed to Eulerian models (which use grid cells that are fixed in place), LMs are known to create minimal numerical diffusion and thus are capable of preserving gradients in tracer concentration. Additionally,Lagrangian integration is numerically stable, meaning that models can take bigger time steps. Furthermore, the Lagrangian framework is a natural way to model turbulence,as it is a closer physical analog to the pathways traced by eddies.

These advantages served as the inspiration from which Lagrangian particle dispersion models (LPDMs) have evolved, in which air parcels are modeled as infinitesimally small particles that are transported with random velocities representing turbulence. LPDMs often track many thousands to millions of particles in three dimensions and are more sophisticated than simple trajectory or puff models. With the availability of computational resources, full three-dimensional LPDM simulations that were expensive to run just a decade ago are now routinely carried out.

Histories of Numerical Climate Models

Meteorology Project, 

Institute for Advanced Study, Princeton, 1952. 

Left to right: Jule Charney, MANIAC I, Norman Phillips, 

Glenn Lewis, N. Gilbarg, George Platzman.

Courtesy AIP Emilio Segrè Visual Archives.

I was recently doing some background reading on the history of general circulation models (GCMS) for a paper and thought I'd share two of the nice histories I found.  The first is one that I've shared with many colleagues, both for information and for inspiration:

General Circulation Models of Climate

ABSTRACT: The climate system is too complex for the human brain to grasp with simple insight. No scientist managed to devise a page of equations that explained the global atmosphere's operations. With the coming of digital computers in the 1950s, a small American team set out to model the atmosphere as an array of thousands of numbers. The work spread during the 1960s as computer modelers began to make decent short-range predictions of regional weather. Modeling long-term climate change for the entire planet, however, was held back by lack of computer power, ignorance of key processes such as cloud formation, inability to calculate the crucial ocean circulation, and insufficient data on the world's actual climate. By the mid 1970s, enough had been done to overcome these deficiencies so that Syukuro Manabe could make a quite convincing calculation. He reported that the Earth's average temperature should rise a few degrees if the level of carbon dioxide gas in the atmosphere doubled. This was confirmed in the following decade by increasingly realistic models. Skeptics dismissed them all, pointing to dubious technical features and the failure of models to match some kinds of data. By the late 1990s these problems were largely resolved, and most experts found the predictions of overall global warming plausible. Yet modelers could not be sure that the real climate, with features their equations still failed to represent, would not produce some big surprise.

And here is one of my favorite passages about the birth of the enterprise:

In 1922, the British mathematician and physicist Lewis Fry Richardson published a more complete numerical system for weather prediction. His idea was to divide up a territory into a grid of cells, each with its own set of numbers describing its air pressure, temperature, and the like, as measured at a given hour. He would then solve the equations that told how air behaved (using a method that mathematicians called finite difference solutions of differential equations). He could calculate wind speed and direction, for example, from the difference in pressure between two adjacent cells. These techniques were basically what computer modelers would eventually employ. Richardson used simplified versions of Bjerknes's "primitive equations," reducing the necessary arithmetic computations to a level where working out solutions by hand seemed feasible. Even so, "the scheme is complicated," he admitted, "because the atmosphere itself is complicated."  

The number of required computations was so great that Richardson scarcely hoped his idea could lead to practical weather forecasting. Even if someone assembled a "forecast-factory" employing tens of thousands of clerks with mechanical calculators, he doubted they would be able to compute weather faster than it actually happens. But if he could make a model of a typical weather pattern, it could show meteorologists how the weather worked. 

So Richardson attempted to compute how the weather over Western Europe had developed during a single eight-hour period, starting with the data for a day when scientists had coordinated balloon-launchings to measure the atmosphere simultaneously at various levels. The effort cost him six weeks of pencil-work Perhaps never has such a large and significant set of calculations been carried out under more arduous conditions: a convinced pacifist, Richardson had volunteered to serve as an ambulance-driver on the Western Front. He did his arithmetic as a relief from the surroundings of battle chaos and dreadful wounds.

The work ended in complete failure. At the center of Richardson's simulacrum of Europe, the computed barometric pressure climbed far above anything ever observed in the real world. "Perhaps some day in the dim future it will be possible to advance the calculations faster than the weather advances," he wrote wistfully. "But that is a dream." Taking the warning to heart, meteorologists gave up any hope of numerical modeling.

I also found this chapter in a Google-book from a decade ago which had a very nice introduction to some of the early experiments and technical innovations.  It's slightly more technical, but extremely succinct. Less history but maybe more science.