J. M. Lewis The Story behind National Severe Storms Laboratory, the Bowen Ratio Norman, Oklahoma
Abstract Qh\ energy given off to the atmosphere as sensible heat (conduction), Ira Sprague Bowen (1898-1973) was a prominent astrophysicist Qs: energy associated with change in mean during the twentieth century. In his impressive oeuvre of work over temperature of the ocean. the 50-year span (1920-70), there appears a lone contribution to the geophysical sciences on the subject of evaporation and conduction from water surfaces. This theoretical development led to an expres- Here Qs is set to zero under the assumption of no net sion for the ratio of heat conduction to evaporative flux at the air- warming/cooling on yearly timescales, and Qc van- water interface, labeled the Bowen ratio by Harald Sverdrup in the ishes for the ocean as a whole. Thus, the annual early 1940s. The circumstances that led to this contribution are radiation surplus is balanced by conduction and evap- examined with attention to the character of education and research oration. In an effort to simplify Eq. (1), Schmidt (1915) at the California Institute of Technology during the 1920s. Bowen was unaware of the important precedent work in meteorology and introduced the ratio fluid dynamics that is also reviewed.
(2) 1. Introduction a
The first quarter of the twentieth century saw the and solved for evaporation as a function of Qrand R; rapid advancement of physical oceanography. Theo- namely, retical developments and conceptual modeling fol- lowed extensive field work from the voyages of the Or Challenger (England, 1872-76) and the Fram (Nor- E = (3) way, 1893-96) (Deacon 1971; Schlee 1973). The data L(UR)' collection from military and commercial ships that led to the Wind and Current Charts (Maury 1848-1860) The radiation surplus could be estimated from also stimulated the science. Among the subjects that climatological distributions of sea surface tempera- began to receive attention was evaporation from the tures, water vapor content of the atmosphere, and World Ocean. cloudiness along with the astronomical parameters The first estimates of evaporation were made by (solar irradiance, solar zenith angle). These calcula- Schmidt (1915) using the energy budget equation for tions of surplus radiation were far from simple and the ocean. Using Sverdrup's notation from the Hand- certainly subject to error. Anders Angstrom spent book of Physics (Sverdrup 1957), the budget equation much effort in refining and trying to improve his esti- is written as mates of radiation. Despite these commendable ef- forts, he said, "my purpose at present is more to show
Qr+Qc=Qe+Qh+Qs (1) how various radiation measurements may be used for studies of convection and evaporation, than to pretend where Q - radiation surplus, to give an exact determination, which at present is not Qc: amount of energy carried by the ocean feasible" (Angstrom 1920, p. 241). currents into a given area, Finding an appropriate value of R was the subject Qe: energy used for evaporation [= L E of much controversy. Following Dalton's seminal work where L is the latent heat of vaporiza- on evaporation (Dalton 1802,1803), English engineer tion and E is the mass (grams) of water Desmond Fitzgerald showed that evaporation was evaporated], proportional to the vapor pressure gradient at the liquid surface (Fitzgerald 1886; Livingston 1908). However, the exact form of the expression was un- Corresponding author address: J. M. Lewis, National Severe Storms Laboratory, 1313 Halley Circle, Norman, OK 73069. known. Taylor (1915) also showed that turbulent con- In final form 27 July 1995. duction of heat was governed by an equation identical
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Unauthenticated | Downloaded 10/10/21 11:44 PM UTC to the molecular process but where molecular conduc- home schooling was necessitated by the constant tivity was replaced by an "eddy conductivity" that was uprooting of the family in response to his father's approximately four orders of magnitude greaterthan its position as an itinerant fundamentalist preacher in the molecular counterpart. Thus, fragmentary information Appalachian region of northern Pennsylvania. His on the form of R was known, but a precise expression father died in 1907 and his mother took a job at a junior was unavailable when Schmidt and Angstrom made college in Houghton, New York. Bowen attended their calculations. Houghton Junior College and came under the influ- The breakthrough in finding an analytical expres- ence of James Luckey, president of the college and sion for R came in 1925-26 at the California Institute teacher. As recalled by Bowen, "He taught mathemat- of Technology (Caltech). The work was accomplished ics and physics and was one of the finest teachers I by a graduate student named Ira Bowen. It was not ever had... he was a graduate of Oberlin [in Ohio] and until the early 1940s that Scripps oceanographer [suggested] I go there" (Bowen 1968). Woodrow Jacobs began to calculate R based on the Bowen received his bachelor's degree at Oberlin in work of Bowen (Jacobs 1942,1943; Bowen 1926a,b). 1918 under the direction of Sam Williams. He remem- Since that time, oceanographers and meteorologists bered Williams as follows: "He was a very poor have adhered to Bowen's formulation with only slight lecturer, but I think he sent more people away for their modification. Sverdrup (1943) termed the "Bowen ratio" doctor's degrees than practically any other person in R. Over the oceans, the ratio varies from about 0.1 in the country, because he was doing a small amount of low latitudes to 0.45 at 70°N and 0.23 at 70°S (Perry research, largely in magnetism and he took all junior and Walker 1977, p. 83). Roll (1965) has explained as and senior students in with him" (Bowen 1968, p. 2). follows: "The difference between the values [of R] for Bowen's first paper was a joint publication with Will- the two hemispheres is ascribed to the influence of the iams and Hadfield on the magnetic properties of large continents of the Northern Hemisphere from manganese steel (Hadfield et al. 1921). which cold air flows out over the oceans in winter." Bowen met Millikan, an Oberlin graduate, during Bowen's work on this ratio was an anomaly in his the 1917-1918 academic year when Millikan visited impressive oeuvre that spanned six decades. His con- his alma mater. Williams encouraged Bowen to apply tributions were primarily in spectroscopy and astrophys- for graduate school at the University of Chicago ics. As a doctoral candidate and assistant to Robert where Albert Michelson and Millikan were luminaries. Millikan in the 1920s, Bowen was primarily concerned He was accepted and became involved with follow-up with spectroscopy; but in 1925, while Millikan was work on Millikan's famous oil-drop experiment. When burdened with institutional matters and involved in Millikan accepted the position as chief executive at cosmic ray research, Bowen was asked to supervise Caltech in 1921, he offered Bowen an instructorship another doctoral candidate in physics, Nephi and later a position as his personal assistant at Cummings. As an adjunct to Cummings's thesis, Caltech's Norman Bridge Physics Laboratory. Bowen developed his now-famous ratio that earned him Thus, in 1921 Bowen ("Ike" to his associates) was the Ph.D. degree. The circumstances that led to this a doctoral candidate at Caltech but also an instructor work are reviewed with some attention to the character and assistant to Millikan. During the period 1921-26, of education and research at Caltech during the period. Bowen coauthored 20 papers with Millikan on atomic spectra and cosmic rays while teaching undergradu- ate physics. [See Babcock (1982) for a complete list of 2. Profile of Ira Sprague Bowen Bowen's scientific publications.] A picture of Bowen, (1898-1973) Millikan, and Julius Pearson is shown in Fig. 1,1
Bowen achieved prominence in astrophysics dur- ing the period 1920-70 and, accordingly, there is a b. Bowen's scientific profile sizable amount of biographical material associated As a backdrop to Bowen's dissertation work, it is with his life and work (Bowen 1968; Osterbrock 1975, instructive to examine the manner in which Millikan 1992; Babcock 1982). This sketch draws from these sources as well as from personal reminiscences from 1Julius and Fred Pearson were Swedish brothers who were hired colleagues Horace Babcock, H. Victor Neher, Donald by Albert Michelson in the early 1900s. They had established Osterbrock, and Harold Wayland. themselves as master craftsmen at Petididier's Optical Shop in Chicago, and Michelson employed them to work on diffraction a. Early training and association with Millikan gratings and other optical devices. Julius followed Millikan to Bowen was home schooled by his mother, a nor- Caltech, while Fred remained with Michelson at the University of Chicago (Livingston 1973). mal school graduate with a license to teach. The
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Unauthenticated | Downloaded 10/10/21 11:44 PM UTC and Bowen interacted during the early to mid-1920s. As recalled by Bowen,
Millikan was very busy, and while he supported [the work] a great deal, he never came around to the laboratory ex- cept to look around. Intact, he often didn't quite know what I was doing until I got ready to write an article and I'd go around and say, 'I've got an article. How about coming around tonight?' He was al- ways busy in the daytime, so he'd appear about nine o'clock and we'd work until midnight writing the article. He always wrote the article, and as I say, he did very little actual work on it, such as taking the plates, measuring them, etc., . . . though he always kept pretty close in touch with it. . . . I tended to [initiate] a lot of the work but he followed it right along (Bowen 1968, pp. 2-3).
As assistant to the director, Bowen was responsible for run- ning the Bridge Physics Labora- tory during Millikan's absences. One 5-page letter in the Caltech Archives (Millikan 1927) gives the flavor of the myriad respon- sibilities assumed by Bowen FIG. I.Leftto right: Robert Millikan, Julius Pearson, and Ira Bowen in the Caltech Instrument durina these absences "Put Shop. They are examining a cosmic-ray electroscope designed by Millikan and Bowen and built [Paul] Epstein in charge Of by Pearson (ca. 1925) (courtesy of the Caltech Archives). the Physics Club while I'm gone . . . send slides of alpha tracks to me . . . push Taylor to get some research "He was pretty much a 'loner' in his work . . . intuitive results." As recalled by Wayland, "It always seemed to rather than mathematical and basically an experi- me that Millikan took real stock in Bowen's opinions on menter. . . . He was solid, but not an inspiring teacher, personnel and scientific matters. My impression was at least in the course I took from him [Optics]" that Millikan depended first on Ernest Watson and (H. Wayland 1994, personal communication). then on Ike Bowen for keeping track of what went on in physics at the Institute" (H. Wayland 1994, personal c. Career path communication). After completing his dissertation on the ratio of Bowen's colleagues (Babcock, Neher, and Wayland) evaporation to conduction, Bowen was appointed remember him as quiet and unassuming but not afraid professor of physics at Caltech and kept that appoint- to speak his mind when it seemed appropriate. Neher ment for the remainder of his career (until 1964); (1993) said, "He was a very clear thinker—someone following World War II, he was appointed director of who was very hard to fool. Better than anyone else I Mount Wilson and Palomar, the astronomical obser- have known, he could look something straight in the vatories jointly administered by Caltech and the eye, and call it by its right name. ... He had a very Carnegie Institution of Washington (Osterbrock 1992). clear way of expressing his ideas." Wayland added, Bowen became a member of the National Academy of
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Unauthenticated | Downloaded 10/10/21 11:44 PM UTC Sciences in 1936 and was the recipient of three ration was primarily set by the amount of radiation that honorary doctorates [Oberlin College 1948, University came in from the sun, and you could take the amount of Lund (Sweden) 1950, and Princeton University of radiation from the sun and divide it by the heat of 1953]. evaporation, and that was it." He will be remembered in the history of science for As one reads Cummings's work (Cummings 1921, unraveling the mystery of the "nebulium" lines in 1925, 1926), it becomes clear that he believed the astrophysics,2 for fundamental contributions to the atmospheric conditions (wind speed, temperature, optical design of the Palomar 200-in. telescope, and and humidity) had little to do with evaporation. for "the ratio." The radiant energy per square centimeter inte- grated over any time interval was equal to the 3. The ratio heat represented by the change in tempera- ture of the water plus the heat represented by the evaporation per square centimeter during a. Angstrom's calculation of R the same time interval, plus a small correction Angstrom parameterized conduction from water to be determined empirically. This correction surfaces in terms of the air-water temperature differ- appears to depend on atmospheric conditions. ence and an empirical coefficient (which he called (Cummings 1925) "convectivity of the air"). He said that this coefficient "depends probably in high degree upon the sign of the Schmidt (1915) estimated Rto range between 0.4 air-water temperature difference, upon the wind ve- and 0.8 for various latitudinal bands, but Cummings locity and upon the nature of the surface itself" relied upon Angstrom's estimate of R (-0.1) as jus- (Angstrom 1920, p. 239). He estimated evaporation in tification for relegating this correction term to zero: terms of the vapor pressure difference over the water "temperature and humidity need enter the calcula- surface, wind speed, temperature, and another empiri- tions [of evaporation] only as terms of relatively small cal coefficient. Using data collected over Lake Vas- correction, which for many purposes can be ne- sijaure (Sweden), Angstrom estimated R to be -0.1. glected entirely" (Cummings 1926). Cummings be- Although empirically grounded, Angstrom's re- came head of the Division of Science at San Bernar- search made it clear that R was controlled by the dino Valley Junior College after obtaining his Ph.D. gradients of temperature and vapor pressure over the from Caltech in 1926. Figure 2 shows Cummings in a water surface. His discussion also leaves the impres- group photo of division heads and administrative staff sion that he knew the work by researchers in turbu- at the college. lence such as Boussinesq and Taylor (Boussinesq 1896; Taylor 1915). In the conclusions to his article, he c. Bowen's derivation of R wrote, "But the values for the turbulence, which we Bowen's 13-page dissertation clearly states the possess, are average values for air layers of consid- motivation for the work in the first paragraph: erable depth, and especially they can not— and this is a point which ought to be emphasized—be applied to The present paper is a theoretical attempt to the limit conditions at the lower boundary." evaluate losses by conduction and convection in terms of easily measurable quantities, and b. Cummings' thesis hence to determine whether they are small Nephi Cummings had worked forthe U.S. Weather enough to be neglected [in the calculation of Bureau but decided to enroll at Caltech in the early evaporation]; and if not, how they may be cor- 1920s to pursue a Ph.D. degree. As mentioned ear- rected. (Bowen 1926a, p. 1) lier, Bowen was assigned as Cummings's thesis advisor. Cummings began to install insulated pans Bowen's use of the word "convection" implies that and tanks of water around the campus and measured he would consider heat transfer in a laminar mode. He evaporation from them. As stated by Bowen (Bowen did not make reference to turbulent transfer. 1968, p. 9), "he [Cummings] had a theory that evapo- Bowen assumed a steady horizontally uniform wind that varied with height (wind directed along the posi- tive xaxis and the height, z, positive upward). Equat-
2ln parallel with the bright yellow line in the sun's spectrum, which ing the advective transport through the lateral faces had been attributed to an unknown element (helium) before the with the net diffusion through the vertical faces, the element was discovered on earth, it had been conjectured that governing equations for the specific energies (heat nebulium was also an unknown but real element in galactic nebulae and latent heat 6) take the form (Babcock 1982, p. 92).
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Unauthenticated | Downloaded 10/10/21 11:44 PM UTC ,, ,de _ d2e convection" (Bowen 1926a). The original notation has (4) been changed to conform with this article. Bowen considered three cases, two of which were special cases. In case 1, a constant wind (=K) blew over the lake between the interface and z = a but d d2 f{Z) l-D, (5) <9x s a. If "a" and "K" are small and the lake large, then the layer of air (depth = a) will have its temperature changed to that of the water and will where f(z) is the wind profile and DE and Ds are the become saturated with water vapor; that is, its spe- molecular diffusion coefficients for vapor and heat, cific heat density will change from 02 to and its latent respectively. The energy 0 and associated with one heat density from ft, to 01. In this case the ratio of heat mole (one Avagadro's number of the molecules in air) lost by conduction to that lost by evaporation is is defined as follows: 01-02 R = (easel). (8) 0 = c;r (6)
In case 2, the wind is assumed to vanish between the interface and z = a but takes on the constant value K G = L (7) above this surface layer. The area of the lake is assumed to be small and the velocity K large. Then where c* is the molar specific heat of air at constant the water vapor and heat diffusing through the sta- pressure [«(7/2)R*], where R* is the universal gas tionary layer will be carried away immediately. Under constant); e and P are the vapor and air pressure, these conditions, the rates that heat and water vapor respectively; and T is the air temperature. Bowen leave the water surface are determined solely by the used different definitions for 6 and ; namely, 6 = diffusion and the ratio between them is pacp7~and 0= Lpw, wherepa and pware the densities of air and water vapor, respectively, and where cp is the specific heat of air at constant pressure. The molar R Ps(0i-02) (case2) (9) forms of energy obviate the need for specifying den- De(0,-02) " sities, and the computations are also simplified. Equations (4) and (5) are solved subject to the boundary conditions:
0=0if 0= 0:a\z=0 (air-water interface)
0 = fi2,0=02 atx=0 (upwind end of body of water).
After introducing the equations, Bowen states, "It is seen at once that (4) and (5) are exactly the same form, the only differences being in the values of DEand Ds, which in fact differ by only a few percent (a relationship predicted by the kinetic theory, DE > Ds). This leads one to expect that heat losses by evaporation and FIG. 2. Photo of Nephi Cummings (fourth from the left in the front row). The photograph diffusion, and by conduction will includes division heads and administrative staff of the San Bernardino Valley Junior College in follow the same laws and will be 1938. Cummings was head of the Science Division (courtesy of San Bernardino Valley College, affected in the same way by California).
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Unauthenticated | Downloaded 10/10/21 11:44 PM UTC The third case assumes a power-law profile for the In light of later research, as reviewed by Goldstein wind, f(z) = Kzn, K constant. Bowen states that the (1969), an appropriate value of n in the expression solution to this problem was "found by Professor for the wind profile is 1/y. For moderate values of the Epstein." Epstein was an Arnold Sommerfeld-trained Reynolds number, the "seventh-root profile" gives a theoretical physicist who came to Caltech in the fall of very fair representation of the change of velocity in the 1921 and remained there throughout his entire career neighborhood of a smooth boundary, but for larger (through the 1940s). He assumed a prominent role in values of the Reynolds number, the exponent must be the foundation of Caltech's physics division, introduc- diminished progressively to 1/s, 1/g, etc., to conform to ing and teaching virtually all the theoretical physics the observations (Goldstein 1969; Sutton 1953, chaps. courses in the early years (Goodstein 1991). 3 and 7). The solution found by Epstein is stated on page 6 of Using the definitions of 0and G [Eqs. (6), (7)], along Bowen's thesis, and the result is used to find an with the expression for L as a function of tempera- expression for P. The solution is derived in the appen- ture, the ratio of heat conduction to evaporative flux is dix since it has not been found in textbooks or the scientific literature. Here G and 0 are functions of both x and z, where the height of the mixed layer or boundary layer in- 1^-02 J creases downstream. Since the distributions of 0, 0 (13) CP(T^T2)P cp(T-\ ~T2)P have identical functional forms, R is independent of x, the distance from the upstream shoreline. This ratio is L(T1)e1-L(r2)e2 L(T){e,-e2)' given by
where T- (T, + Tz)/2 and L(T) is given by
4 -1 -Dc L(T) = (4.504(10 )-42.17(°C))J mole . (14) R = z=0 -DE I? When the mean temperature is taken as the triple- dz)z=Q (10) point temperature for water (T= 0°C) and given that 1 c* = 29.099 J(mole K)-\ Bowen obtains K n+2
(n + 2) Dsx f ^ _ 29.099P0(r1-72) 1 : 0.491 A 4 P ,(15) Q^-Qz 4.504(l0 )(e1-e2) \ oj K n+2 DE(d,-d2) (n + 2) DEx (T, A = -7k] where e lei ~ 2 Ju , n+1 n+2 and P0 is the standard air pressure at mean sea level Ds) r* (11) (=760 mm Hg), T is temperature expressed in de- De) -e2) 1*1 grees Celsius, and air pressure (P) and vapor pres- sure (e) are expressed in millimeters. If we choose Bowen argued that n < 0 is physically unreason- a mean water temperature of 12°C, which is more able since it would lead to an infinite velocity at the appropriate for midlatitudinal sea surface tempera- interface; for n > 0 (recalling that DJDE < 1), ture in winter, the coefficient of A in (15) changes to 0.497. 2 -1 Bowen assumed DE = 0.206 cm s , Ds = 0.182 cm2 s-1 [close to the values quoted in List (1966), 01-02 when (01 - 02)/(^ - G2) > 0. The left-hand side of expression (12) corresponds to case 2 (the equivalent 0.43A 2382 Vol. 76, No. 12, December 1995 Unauthenticated | Downloaded 10/10/21 11:44 PM UTC When the diffusivities from List (1966) are used in evant to his research. The work in evaporation was conjunction with a mean temperature of 12°C, the conducted by Jeffreys (1918), while the fluid dynamics limits change to 0.41 A and 0.45/1. work came from Stanton and Pannel (1915). Jeffreys became interested in turbulent diffusion through association with G. I. Taylor at the British 4. Jacobs' use of Bowen's ratio Meteorological Office in the pre-WWI years (Jeffreys 1986, pp. 4-5). Photographs of both men appear in In his work on evaporation over the Pacific and Fig. 3. In Jeffrey's study of evaporation, the governing Atlantic Oceans, Jacobs (1942,1943) used R= 0.50A equation was identical to the one used by Bowen [Eq. [Eq. (11-1) in Jacobs (1942)]. He essentially assumed (4)], except that Jeffreys considered the turbulent DJDe= 1 and T~ 12°C. The equality of diffusivities regime and accordingly used the eddy diffusivity. was consistent with Taylor's arguments regarding Jeffreys found an analytic solution to the diffusion turbulent diffusion (Taylor 1927). Jacobs's estimates equation under the assumption that DE/f(z) was of T2, e2 were those at the height of a ship's bridge, constant. (Since both wind and turbulent diffusivity typically 5-10 m above sea level; T, was the sea generally increase away from the boundary, the as- surface temperature, and e1 the saturation value of sumption is consistent with observation. The resulting vapor pressure associated with this water tempera- solution corresponds to n = 0 in Bowen's case 3.) ture. Jacobs has thoroughly summarized his research Jeffreys found that the latent heat flux was _ V2 on evaporation (and the Bowen ratio) in his well- (02 0:)[DEf(z)/7tx] (in present notation). Applying known review article Energy Exchange Between the the same dynamics to the heat conduction equation, 1/2 Sea and Atmosphere (Jacobs 1951). Seasonal val- R assumes the form (DS/DE) (02- Bulletin of the American Meteorological Society 2381 Unauthenticated | Downloaded 10/10/21 11:44 PM UTC FIG. 3. (left) G. I. Taylor on the roof of the British Meteorological Office in London Tower. Photo was taken by H. Jeffreys in 1919 (courtesy of the Cambridge University Library), (right) Harold Jeffreys in his room on staircase A, St. John's College (ca. 1925) (courtesy of Lady Bertha Jeffreys). ered such refinements, the assumption of no slip at the heat transfer from the fluid to embedded bubbles that air-water interface should also be relaxed (assump- are the product of boiling. tion for deriving the profile in the viscous sublayer next to a rigid plate or pipe). In practice, the velocity will not vanish at a fluid interface. Flow in the water would be 6. Subsequent developments related to induced by the drag of the air at the air-water inter- the Bowen ratio face, and the air would stick to the moving water. Nondimensional numbers abound in fluid dynamics and heat transfer. Thus, one suspects that an equiva- Although this paper concentrated on the use of lent to the Bowen ratio may have appeared in engi- the Bowen ratio in oceanography, it has certainly neering applications. However, a review of the engi- enjoyed widespread use in meteorology, particularly neering literature indicates that the Bowen ratio is micrometeorology/boundary layer meteorology. On cited for problems that involve both heat conduction the micrometeorological timescale of an hour, the and evaporation (cooling towers, for example) ratio varies from minus infinity to zero to plus infinity, (Rohsenow et al. 1985a, sec. 10). A nondimen- normally twice per day (Lettau and Davidson 1957). sional quantity closely relatated to the Bowen ratio Just as the Bowen ratio assumed an important role was introduced in the 1930s under the name "Jacob in the estimate of oceanic evaporation, it has been number" (Rohsenow et al. 1985b, sec. 1). (The num- central to climatological studies over the planet (Budyko ber was named in honor of Max Jacob, late professor 1958; Hare and Hay 1971). Lettau (1980) has esti- of mechanical engineering at the Illinois Institute of mated that a representative value for R over the North- Technology.) This number is used in the study of ern Hemisphere is 0.20, an area composite from land boiling where the conduction of heat from the walls of (0.32) and sea (0.12). An interesting application to a pipe to the confined fluid is compared to the latent climatology was made by Lettau (1969) when he solved 2382 Vol. 76, No. 12, December 1995 Unauthenticated | Downloaded 10/10/21 11:44 PM UTC the water balance equation for land areas and in the process derived the following expression involving the Bowen ratio and two other nondimensional numbers: (1 +fl)(1 -C) = D, where C is runoff/precipitation and D is radiation surplus (at ground)/ (L x precipitation). This equation was derived from the time-averaged surface energy balance equation and the correspondingly aver- aged water-mass balance equation for the soil. Lettau and Hopkins (1991) have used the nondimensional relationship in studies of monthly balances of evaporable water and runoff reduction caused by rain forest depletion in tropical Panama. Their study indicated that a 20% forest deple- tion in the Rio Chagres Basin, Panama, FIG. 4. Heinz Lettau (left) is pictured with (left to right) Paul Mildner, Vilhelm Bjerknes, and Ludwig Weickmann at Leipzig University on the occasion of the 25th over the five-decadal period 1930-79, anniversary of the Leipzig Institute (1938) (courtesy of H. Lettau). resulted in a corresponding reduction of the Bowen ratio from 0.88 to 0.48. Heinz Lettau is pictured in Fig. 4. identity separate from physics. During the later decades of the century the profession devel- oped socially and intellectually independent of physics. . . . One could no longer assume that 7. Epilogue meteorology was a mere appendage of phys- ics. (Garber 1976) In his oral history interview with physicist Charles Weiner, Bowen reminisced about the work on the ratio The same could be said of oceanography and in a very modest and unassuming manner (Bowen geophysics generally (Burstyn 1975; Schlee 1973; 1968). His interest in evaporation/conduction was Schneer 1979). secondary to his research in spectroscopy. But as The ratio as developed by Bowen turned out to be Cummings's thesis advisor, he "looked at the evapo- applicable to the turbulent flow regime since the ratio ration problem straight in the eye," as Victor Neher of the diffusivities in the molecular and turbulent would say, and knew that Cummings's correction term regimes are -1 and the power-law profile is in reason- had to be explained physically. He intuitively wrote able agreement with the "law of the wall." Thus, 25 down the form of the ratio (cases 1 and 2) and enlisted years after Wilhelm Schmidt made his pioneering the services of mathematical physicist Paul Epstein to studies of evaporation with crudely estimated values find the more general solution (case 3). In 1926, of R, Woodrow Jacobs used Bowen's ratio to more Millikan asked Bowen to defend his research for the definitively determine evaporation from the world sea. doctoral degree, and as remembered by Bowen (1968): The ratio possesses both simplicity and robustness "When I got ready to take my degree, that was the and it has admirably served meteorologists and ocean- paper [The Ratio of Heat Losses by Conduction and ographers for over 50 years. Evaporation from Any Water Surface] that was going to press, so it became my thesis." Acknowledgments. I am most grateful to the staff of Caltech Bowen was apparently unaware of important pre- Archives (Archivist Judith Goodstein, Associate Archivist Shelly cedent work in fluid dynamics (turbulence) and meteo- Irwin, and Administrative Assistant Bonnie Ludt) for making my rology that had bearing on his research. This appears several visits to the archives most productive and pleasant. Others consistent with historical research by Elizabeth Garber, who deserve credit are Bowen's colleagues (H. Victor Neher and Horace Babcock), junior colleague (Don Osterbrock), and Bowen's who said, student (Harold Wayland) for writing letters of reminiscence that gave me insight into Bowen's personality and his approach to Even in the middle decades of the nineteenth science; Jim Purser for his solution to the diffusion equation that century meteorology struggled to maintain an is found in the appendix (Bowen's case 3) and Bob Davies-Jones Bulletin of the American Meteorological Society 2381 Unauthenticated | Downloaded 10/10/21 11:44 PM UTC for carefully checking all equations in the manuscript; Charlie Moore for suggesting that the molar form of the energies be used n+2 in the development; reviewers Sterling Colgate, David Stensrud, exp Kg Thomas Rossby, Alan Shapiro, and an anonymous physicist; h = A )dg Mechanical Engineering Department at Oklahoma University, es- (n + 2) D pecially William Sutton and Daryl Hammack, for alerting me to the importance of Bowen's ratio in the engineering sciences; American Institute of Physics for making the transcript of Bowen's oral history The lower limit of the integral has been set to zero to interview available to me; Craig Bohren for alerting me to the satisfy the boundary condition /?(0) = 0. interesting paper by Elizabeth Garber; photo acquisition assis- We simplify the integrand by the substitution, tance from Deborah Axelson (San Bernardino Valley College), Bertha Jeffreys, and E. S. Leedham-Green (Cambridge Univer- 1 sity); and Mary Meacham, librarian at National Severe Storms n+2 Laboratory, and librarians at Environmental Research Labs in K a = Boulder, Colorado, for facilitating interlibrary loan service. (n + 2) D to obtain Appendix: Solution to KzndQ/dx = Dd2qldz2, Bowen's Case 3 ln+2 (n+2)2 Dx j In a problem of this form, it is natural to seek a n+2 m h = A* exp(- m The scaling factor A* is given by Gx = mzx ^h' m 0 -0-\ ez = x h' 2 J exp -an+2 da 2m 0zz = x h", where h' and h" are the first and second derivatives of to yield the proper asymptotic behavior, h(g) h with respect to g. Substituting these expressions into as g -» Kznd0/dx= DcPO/rJz2, we obtain References mK zn+1 h" D x /77+1 Angstrom, A., 1920: Applications of heat radiation measurements to the problems of the evaporation from lakes and heat convection at their surfaces. Geogr. Ann., 2, 237-252. But for h"/lf to be a function only ofg, that is, h"/h' a gp, Babcock, H. W., 1982: Ira Sprague Bowen (1898-1973). Biogr. we require m = -M(n + 2). Then -(K/(n + 2)D)g^ = Mem. Nat. Acad. Sci., 53, 83-119. 2382 Vol. 76, No. 12, December 1995 Unauthenticated | Downloaded 10/10/21 11:44 PM UTC , 1925: The relative importance of wind, humidity, and solar Livingston, D. M., 1973: The Master of Light (A Biography of Albert radiation in determining evaporation from lakes. Phys. Rev., A. Michelson). Scribner's Sons, 264 pp. 25, 721. Livingston, G. J., 1908: An annotated bibliography of evaporation. , 1926: Evaporation from lakes. Ph.D. dissertation, California Mon. Wea. Rev., 36, 181-186, 301-306, 378-381. Institute of Technology, 20 pp. , 1909: An annotated bibliography of evaporation. Mon. Wea. Dalton, J., 1802: Experimental essays on the constitution of mixed Rev., 37, 68-72,103-109, 157-160, 193-199, 248-252. gases; on the force of steam or vapor from water and other liquids Maury, M. F., 1848-1860: Wind and Current Charts. Library of in different temperatures, both in a Torricellian vacuum and in air; Congress (Manuscripts Division), Washington, DC. on evaporation and on the expansion of gases by heat. Mem. of McEwen, G. F., 1938: Some energy relations between the sea Manchester Lit. and Phil. Soc., 5, 535-602. surface and the atmosphere. J. Mar. Res., 1, 217-238. , 1803: Experiments and observations made to determine Millikan, R. A., 1927: Letter to I. S. Bowen, 30 March 1927. Millikan whether the quantity of rain and dew is equal to the quantity of Collection, Folder 37.23, Cal Tech Archives, CIT Libraries, water carried off by rivers, and raised by evaporation; with an Pasadena, CA, 4 pp. inquiry into the origin of springs. Ann. Physik, 15, 249-278. Mossby, H., 1936: Verdunstung und Strahlung auf dem Meere Deacon, M., 1971: Voyage of H.M.S. Challenger. Scientists and the (Evaporation and Radiation from the Ocean). Ann. Hydrog. Sea (1650-1900: A Study of Marine Science), Aberdeen Univer- Marit. Meteor., 64, 281-286. sity Press Ltd., 333-365. Neher, H. V., 1993: Memories (Autobiography). Published by au- Fitzgerald, D., 1886: Evaporation. Trans. Amer. Soc. Civ. Engr., 15, thor, 292 pp. 581-645. Osterbrock, D. E., 1975: IraSprague Bowen. Dictionary of Scientific Garber, E., 1976: Thermodynamics and meteorology. Ann. Sci., Biography, Vol. 17 (Suppl. II), C. C. Gillispie, Ed., Scribner's 33,51-65. Sons, 95-96. Goldstein, S., 1969: Fluid mechanics in the first half of this century. , 1992: The appointment of a physicist as director of the Annu. Rev. Fluid Mech., 1,1-28. astronomical center of the world. J. Hist. Astron., 23,155-165. Goodstein, J. R., 1991: Millikan's School (A History of the Califor- Panofsky, H. A., and J. A. Dutton, 1984: Atmospheric Turbulence. nia Institute of Technology). Norton and Co., 317 pp. Wiley-lnterscience, 364 pp. Hadfield, R., S. R. Williams, and I. S. Bowen, 1921: The magnetic Perry, A. H., and J. M. Walker, 1977: The Ocean-Atmosphere mechanical analysis of manganese steel. Proc. Roy. Astron. System. Longman Publishing Co., 160 pp. Soc., 98, 297-302. Rohsenow, W. M., J. P. Hartnett, and E. N. Ganic, 1985a: Handbook Hare, F. K.,and J. E. Hay, 1971: Anomalies in the large-scale annual of Heat Transfer (Fundamentals). McGraw-Hill, 624 pp. water balance over northern North America. Can. Geogr., 15, , , and , 1985b: Handbook of Heat Transfer {Applica- 79-92. tions). McGraw-Hill, 408 pp. Jacobs, W. C., 1942: On the energy exchange between sea and Roll, H. U., 1965: Physics of the Marine Atmosphere. Academic atmosphere. J. Mar. Res., 5, 37-66. Press, 426 pp. , 1943: Sources of atmospheric heat and moisture over the Schlee, S., 1973: The Edge of an Unfamiliar World. E. P. Dutton and North Pacific and North Atlantic Oceans. Ann. N.Y. Acad. Sci., Co., 398 pp. 44,19-40. Schlichting, H., 1979: Boundary Layer Theory. 7th ed. Translated , 1951: The Energy Exchange between Sea and Atmosphere by J. Kestin, McGraw-Hill, 817 pp. and some of its Consequences. University of California Press, Schmidt, W., 1915: Strahlung und Verdunstung an freien 122 pp. Wasserflachen, ein Beitrag zum Warmehaushalt des Weltmeers Jeffreys, H., 1918: Some problems of evaporation. Phil. Mag. (sixth und zum Wasserhaushalt der Erde (Radiation and evaporation series), 35, 270-280. from an open water surface, a contribution to the heat budget of , 1986: Interview by Dr. M. E. Mclntyre, Cambridge, England, the world oceans and to the water budget of the earth). Ann. 16 September 1986,20 pp. [Available from the National Meteo- Hydrogr. Mar. Meteor., 43,111-124. rological Library, London Rd., Bracknell, Berkshire RG12-2SZ, Schneer, C. J., 1979: Two Hundred Years of Geology in America. UK.] University Press of New England, 385 pp. Lettau, H., 1969: Evapotranspiration climatonomy I. A new ap- Stanton, T. E., and J. R. Pannel, 1915: Similarity of motion in proach to numerical prediction of monthly evaportranspiration, relation to the surface friction of fluids. Proc. Roy. Soc. London, runoff, and soil moisture storage. Mon. Wea. Rev., 97,691-699. Ser. A, 91, 46-64. , 1980: Course notes in climatonomy, Meteorology 503. Univer- Sutton, O. G., 1953: Micrometeorology. McGraw-Hill, 333 pp. sity of Wisconsin Meteorology Department Handout 11. [Avail- Sverdrup, H. U., 1943: On the ratio between heat conduction from able from J. Lewis, NSSL, 1313 Halley Circle, Norman, OK the sea surface and heat used for evaporation. Ann. N. Y. Acad. 73609.] Sci., 44, 81-88. , and B. Davidson, 1957: Exploring the Atmosphere's First Mile. , 1957: Oceanography. Handbuch der Physik (Geophysik II), Vols. I and II, Pergammon Press, 378 pp. 68, 608-670. , and E. J. Hopkins, 1991: Evapoclimatonomy III: The recon- Taylor, G. I., 1915: Eddy motion in the atmosphere. Phil. Trans., ciliation of monthly runoff and evaporation in the climatic A215, 1-26. balance of evaporable water on land areas. J. Appl. Meteor., , 1927: Turbulence (Symons Memorial Lecture delivered to the 30, 776-792. Royal Meteorological Society on March 16,1927). Quart. J. Roy. List, R. J., Ed., 1966:Meteorological Tables. Smithsonian Misc. Col- Meteor. Soc., 53, 201-211. lection, Vol. 114,6th ed., Smithsonian Institution Press, 527 pp. Bulletin of the American Meteorological Society 2381 Unauthenticated | Downloaded 10/10/21 11:44 PM UTC Systems, Data, and Environmental Applications Conceived by the Environmental Satellite, Data, and Information Services of NOAA to commemorate the 25th anniversary of the first weather satellite's launch, this volume provides a comprehensive survey of environmental remote-sensing applications that would be useful to both students and scientists. The book is a carefully integrated synthesis of the work of more than 100 scientists, and contains over 400 black-and-white and color illustrations, and extensive bibliographic material ICAN 0 1 TY mm^y 1990, hardbound, 516 pp $95 list/$75 members/$59 sfu^^P includes shipping and handling. * Please send all prepaid orders to: Order Department, AMS, 45 Beacon Street, Boston, MA 02108-3693 2382 Vol. 76, No. 12, December 1995 Unauthenticated | Downloaded 10/10/21 11:44 PM UTC