Bjerknes Founds Scientific Weather Forecasting

Date July, 1897-July, 1904

Vilhelm Bjerknes developed and tested the first hydrothermodynamic mathematical model capable of making weather predictions, thereby transforming weather forecasting from an arcane art into the modern science of meteorology.

Also known as Computational hydrodynamics

Locale Stockholm, Sweden

Key Figures

• Vilhelm Bjerknes (1862-1951), Norwegian theoretical physicist and quantitative meteorologist
• Nils Ekholm (1848-1923), Swedish aeronomist and experimental meteorologist
• J. W. Sandstrøm (1874-1947), Swedish postdoctoral student in fluid dynamics and atmospheric geophysics

Summary of Event

The gradual development of modern predictive meteorology—which employs only empirical observation and mathematical analysis—was the result of a complex interaction of technological, scientific, and military-economic factors. During the nineteenth century, earlier efforts at studying weather processes predominantly used historical data statistics (the rudiments of so-called synoptic meteorology) and personal experience. The would-be forecaster learned to infer roughly how a weather system—then defined by crudely mapping field measurements of barometric pressure near the earth’s surface—would move or change character. Such inferences were generally inaccurate.

Following the near destruction of both the French and British fleets in the Black Sea during the Crimean War (1853-1856), telegraphy became more widely used to disseminate the relatively sparse atmospheric information then available. However, even after the International Meteorological Committee began making efforts in 1873 to standardize, synchronize, and increase observational stations to facilitate international meteorological data exchange, predictions remained neither detailed nor specific as to time and location. Indeed, they typically amounted only to very general forecasts (for example, dry, changeable, or wet), and coastal gale warnings for broad areas were made at most only eighteen hours in advance.

After three decades of empirically studying the formation and progression of large-scale weather systems, by the end of the nineteenth century, meteorologists had reaped only a meager harvest in terms of organized theory and improved predictive capability. Although several separate hydro- and thermodynamic theories for idealized atmospheric conditions had been advanced, these theoretical efforts were divorced almost entirely both from practical forecasting requirements and from detailed physical understanding of the complex processes actually responsible for the change and motion of weather phenomena. Some meteorologists went so far as to abandon completely the possibility of improving rational weather prediction.

Several technological advances and political events, however, brought a new impetus to a new generation of physical meteorologists and oceanographers. These advances included a more widespread network of greater economic and military requirements, as well as opportunities for meteorological observations and predictions of greater geographic extent and accuracy. Other motivations for developing meteorology included the associated aerodynamic stimuli to enhance theories of aerodynamic fluid flow for improved aircraft construction and, independently, attempts at theoretical mechanization of electromagnetic wave fields via quantitative analogues with hydrodynamics. The latter were developed by the physicists Heinrich Hertz , Philipp Lenard, Carl Anton Bjerknes, and his son, Vilhelm.

Despite general neglect by the physics community at large, the Bjerkneses concentrated on the problem of formulating a complete and common set of equations for electromagnetic and hydrodynamic force and flux fields. One of the chief analogues was the mathematical similarity between fluid and electromagnetic “solenoids of circulation.” When, in July, 1897, Vilhelm Bjerknes first presented his two extensions of Lord Kelvin’s circulation theorems in a lecture to the Stockholm Physics Society, he mentioned no applications whatsoever. Soon after, Bjerknes was approached by his colleagues Nils Ekholm and Svante August Arrhenius, experts in aeronomy and meteorology, respectively, concerning the potential applications of Bjerknes’s fluid mechanical analogues to the quantitative study of meso-scale atmospheric motions. As evidenced by Bjerknes’s subsequent 1898 lecture and paper “On a Hydrodynamic Circulation Theorem and Its Application to the Mechanics of the Atmosphere and Global Oceans,” Bjerknes had begun to consider circulation-theorem applications to polar and continental atmospheric and ocean-flow phenomena.

From 1850 to 1905, it was widely believed that so-called extratropical cyclones were initiated solely by local thermal motion and maintained by the liberated thermal heat of convection. In 1891, Ekholm had shown empirically that the atmosphere frequently has characteristics similar to those of the fluid later postulated by Bjerknes for his electrohydrodynamic circulation theorems. Most noticed by Ekholm in 1898 was the incongruity between lines of equal value of pressure and density in the vicinity of cyclonic (low-pressure) systems. In response to these suggestions (and the receipt of unique upper-air data recording the passage of a cyclone and anticyclone over the Blue Hill Observatory near Weston, Massachusetts), Bjerknes, together with his assistant J. W. Sandstrøm, returned to the circulation theorems, now directly analyzing them from a geophysical applications perspective rather than electromagnetic analogy.

During his initial studies, Bjerknes generalized the previous propositions of Kelvin and Hermann von Helmholtz on the velocity of circulation and conservation of vorticity. Bjerknes’s generalization was based on introducing a broader interpretation of the definition of fluids. Whereas earlier views assumed a unique (hydrodynamic) relationship between pressure and volume, in his publications “The Dynamic Principles of Circulation and Motion in the Atmosphere” (1900) and “Circulation Relative to the Earth” (1901), Bjerknes expanded his circulation theorem further to its now-classic form by including terms for Coriolis forces arising from the earth’s rotation and approximations for viscous-thermal losses caused by friction from the atmospheric fluid. Using their equations, Bjerknes and Sandstrøm were theoretically able to reconstruct successfully the changes in direction and intensity of the Massachusetts low-pressure system. Although constructed in retrospect, this reconstruction is believed to be the first scientific “prediction” of weather phenomena in history.

Except for acoustic waves, all atmospheric motions may be characterized as flow circulations along closed streamlines. The area distribution of horizontal atmospheric velocity may be represented in terms of two scalar quantities: relative vertical vorticity and horizontal divergence. The former is twice the angular velocity of an air particle around a vertical axis relative to the earth. The latter is the relative expansion rate of an infinitesimal horizontal area moving with the air. The horizontal velocity field can be decomposed mathematically into one horizontal component containing all the vorticity and no divergence and likewise into another all-divergence/no-vorticity component. These two components of total atmospheric air mass motion have different behaviors. For example, whereas small-scale convection and internal-gravity waves are associated with the first component, large-scale atmospheric motions of interest to international forecasting are predominantly controlled by the latter, revealed by isobaric contour maps having predominantly horizontal circulations and, hence, vorticity-component dominance.

In Bjerknes’s initial geometrical interpretation of his circulation theorems as a series of solenoids, because of the tendencies toward rotation in the crisscross lattice of intersecting surfaces, occurrence of skewed distributions of pressure and density should result in overall spatial circulation. Bjerknes’s circulation theorem also can explain smaller-scale reciprocating air circulations, such as land-sea breezes and mountain-valley winds. In both cases, circulation is maintained to satisfy the basic vorticity continuity and conservation conditions. Because of radiative heating, mountain slope air temperature increases more in the daytime than does air temperature at equal pressure away from the mountain. Consequently, there arises a day wind blowing up the slope and a night wind blowing downward, as first rigorously demonstrated by Julius Wagner von Jauregg in 1932 using Bjerknes’s continuity equation.

In Lehrbuch der rosmischen Physik (1903; treatise of cosmic physics), Arrhenius was the first to include independently Bjerknes’s circulation theorem as the basis for a chapter on the thermomechanics of the atmosphere and oceans. Later in 1903, Bjerknes himself explicitly formulated and published a major proposal for predicting weather rationally. The proposal was more fully explained in his July, 1904, publication Das Problem der Wettervorhersage, betrachtet vom Standpunkte der Mechanik und der Physik (the problem of weather prediction considered from the standpoint of mechanics and physics). These latter publications outline two basic conditions for an improved predictive meteorology based on his prognostic circulation equations: sufficient knowledge of the state of the atmosphere at a given place and time based on a sufficient number of accurate measurements, and sufficiently accurate knowledge of the quantitative physical laws by which one atmospheric state at a given place and time evolves into another.

Since manual solution of equations over many separate observation (grid) points and times was practically impossible (until the advent of computers), Bjerknes and Sandstrøm suggested employing a physical-graphical approximation method. To evaluate the resulting circulation integrals, approximate two-dimensional surfaces of equal pressure (isobars) and of equal specific volume (1/density = isosters) were drawn at specified regular intervals. These surfaces subdivide the three-dimensional atmospheric space into tubes of isobaric-isosteric solenoids. It can be shown, through application of Stokes’s theorem of integral calculus, that the integration value is equal to the number of solenoids enclosed by the curve around which the circulation integral is taken.

Significance

Although a number of British and German observational meteorologists before him had varyingly suggested that cyclones could be associated with regional motion of large-scale circulation air bodies, these anticipations were formalized and subsumed in Vilhelm Bjerknes’s work. Because they not only included rigorous derivations and predictions but also tied these to the best available observational data, as underscored by Hans Ertel, Bjerknes’s publications had a greater impact on reconceiving the atmosphere as multiple dynamically related air masses instead of a unified global static air mass than the earlier (1903) but purely theoretical hydrodynamic studies of French physicist Jacques Hadamard. In addition to becoming the object of further theoretical efforts to reprove and improve its formulation, Bjerknes’s circulation theorems not only became the basis of his later Bergen School of dynamic meteorology but also had the greatest impact on German, French, British, and American quantitative meteorology.

In addition to Vilhelm and his son Jacob’s publications (1910 and 1918, respectively) on atmospheric flow-line convergence and divergence in cloud/precipitation formation and cyclonic squall-lines, in 1921, Jacob Bjerknes and Halvor Skappel Solberg extended this work in Meteorological Conditions for the Formation of Rain, introducing the concepts of warm and cold fronts into predictive meteorology. A year later, they published Life Cycle of Cyclones and the Polar Front Theory of Atmospheric Circulation (1822), in which their prior descriptive model of cyclones was shown to be a special case, or rather a single stage, in the genesis and development of cyclones, from incipient unstable atmospheric waves through occluded/stalled fronts and dying frontal vortices.

Notwithstanding the fact that polar fronts do not account for all low-pressure systems, much of the conceptual and theoretical apparatus as well as nomenclature developed by the Bjerkneses and their colleagues remains intact in contemporary pedagogic and predictive meteorology. Further confirmatory and developmental studies by Tor Bergeron in 1926 and by Carl-Gustaf Arvid Rossby, Erik Herbert Palmén, and others in the 1930’s more closely defined additional frontal and cyclonic phenomena and locally predictive models by developing the kinematic principles of air-mass analysis.

Bibliography

Bates, Charles C., and John F. Fuller. America’s Weather Warriors, 1814-1985. College Station: Texas A&M Press, 1986. Discusses the development and application of the Bergen School’s efforts of fifty years of military weather predictions.

Bjerknes, Vilhelm, and Johann Sandstrøm. Dynamic Meteorology and Hydrography. Vol. 1. Washington, D.C.: Carnegie Institution, 1910. Discusses the theoretical derivations, experimental confirmations, and potential applications of the circulation theorems to predicting atmospheric conditions. Illustrated with numerous maps and diagrams. Written at a higher technical level requiring a solid undergraduate background in partial differentiation equations and/or hydrodynamics.

Cox, John D. Storm Watchers: The Turbulent History of Weather Prediction from Franklin’s Kite to El Niño. Hoboken, N.J.: John Wiley & Sons, 2002. Comprehensive history of weather prediction includes a chapter on Vilhelm Bjerknes, Lewis Fry Richardson, Jacob Bjerknes, Tor Bergeron, Carl-Gustaf Rossby, and Sverre Petterssen.

Friedman, Robert Marc. Appropriating the Weather: Vilhelm Bjerknes and the Construction of a Modern Meteorology. Ithaca, N.Y.: Cornell University Press, 1989. Friedman traces in nonmathematical detail the historical-conceptual details of the revolution in meteorology initiated by Bjerknes. Friedman’s philosophical thesis is that Bjerknes “appropriated” the tools of hydrodynamics and the problems of synoptic meteorology to construct a new predictive meteorology.

Holmboe, Jorgen, George E. Forsythe, and William Gustin. Dynamic Meteorology. New York: John Wiley & Sons, 1945. Basic textbook used to instruct flyers and meteorologists. Develops Bjerknes’s basic thermohydrodynamic principles directly from physical concepts.

Kutzbach, Gisela. The Thermal Theory of Cyclones: A History of Meteorological Thought in the Nineteenth Century. Boston: American Meteorological Society, 1979. Presents a thematic analysis of the historical evolution of Euro-American meteorology. Discusses Bjerknes’s numerical-observational predictive program from 1903 to 1905.