Vertical Eddy Diffusion Coefficient Research Articles

Natural radon and phosphorus as limnologic tracers: Horizontal and vertical eddy diffusion in Greifensee

Two‐dimensional interpretation of monthly measurements of natural radon‐222 at different stations in Greifensee, Switzerland, results in hypolimnetic vertical and horizontal eddy diffusion coefficients (Kz and Kx) of 0.2–0.05 and 1,000–100 cm2 s−1 during the stagnation period in 1975. Application of the one‐dimensional and three‐dimensional horizontally well mixed models to the data from the midlake station produces errors of about a factor of two in the vertical eddy diffusion coefficient. With the hypolimnion mixing information, Kz in the thermocline is estimated to be 0.025 ± 0.015 cm2 s−1 by using dissolved phosphorus as a quasi‐conservative tracer.The eddy diffusion coefficients calculated are in good agreement with those which would be predicted by empirical methods. The results when applied to phosphorus cycling indicate that P reflux from the hypolimnion and thermocline in eutrophic Greifensee is of the same magnitude as external inputs during the months of maximum photosynthesis.

A numerical study of tropospheric photochemistry using a one-dimensional model

A numerical study of the tropospheric ozone budget is conducted by using a one-dimensional model which takes into account both diffusion and photochemical processes. It is shown that if ozone is treated as an inert species in the troposphere, large vertical eddy diffusion coefficients and an ozone flux from the stratosphere more than twice that given by Fabian and Pruchniewicz (1976) and Danielsen and Mohnen (1977) must be used to reproduce the observed tropospheric ozone profiles in the northern hemisphere mid-latitudes during the summer. Furthermore, consideration of the reactions which destroy ozone in the troposphere would lead to the destruction of about half of the ozone injected in the troposphere. Thus it is likely that there are also reactions which produce ozone in the troposphere, and we examine the possibility that methane oxidation reactions are responsible for this production (Crutzen, 1974a). Indeed, we show that a model which includes both the aforementioned photochemistry and prescribed physical processes can reproduce the observations reasonably; however, the uncertainty of certain reaction rate constants and the lack of understanding of the tropospheric odd nitrogen budget prohibit the quantification of the tropospheric ozone budget. On the other hand, the model results suggest that the time scales of both the physical and photochemical processes are both of the order of 1–3 months. It is therefore certainly not easy to infer the effects of this slow, but ever present, photochemistry from ozone measurements, and it is understandable why it has gone undetected previously.

Stratospheric Nitrous Oxide Altitude Profiles at Various Latitudes

Abstract A number of N2O profiles obtained in the troposphere and stratosphere at five latitudes are reported. The variability in the reported stratosphere N20 mixing ratios is substantial and indicates a strong dependence on both stratospheric transport and photochemistry. A profile obtained at Panama indicates a relatively large transport of N2O into the stratosphere at low latitudes. This profile represents the first one obtained in the tropics. From the observed data, area-averaged, global vertical eddy diffusion coefficients were derived that were found to be a factor of 1.5 to 3 times larger than those derived by Hunten from data obtained at locations not including the tropics. The derived eddy diffusion profile is heavily weighted by one single profile in the tropics and more observations are needed to substantiate this finding. The estimated flux of N20 into the stratosphere was equal to 15×1012 g(N) per year and the total stratospheric production of NOx was estimated to be 1.6×1012 g(N) per year....

An oxygen-hydrogen atmospheric model and its application to the OH emission problem

An improved time-dependent mesospheric model has been constructed in an attempt to explain more quantitatively the main features of the OH emission. Vertical transport processes are taken into account by means of a height-dependent vertical eddy diffusion coefficient. The oxygen-hydrogen photochemical scheme employed is described in detail. The photochemistry is extended to take account of the different excited vibrational levels of OH which is assumed to be produced preferentially in the upper levels by the hydrogen-ozone reaction. On this basis, important characteristics of the observed emission are correctly predicted, including the rapid intensity decrease before sunrise, the midday maximum (comparable to the nighttime value) and the evening minimum following sunset. As with other published models, the predicted OH nightglow intensity decreases steadily throughout the night in disagreement with the generally erratic intensity variations observed at mid-latitudes. It is shown that changes in dynamic conditions, simulated by temporal variations of K by a factor of 10, produce variations in emission intensity by a factor as high as 1.8 and consequently it is concluded that changes in the dynamic structure of the emission region may be responsible for the longer term nighttime deviations from the simple model. The predicted height profiles of OH† concentration for high and low vibrational levels are quite different by day, with the former extending downward as low as 50–60 km, while the latter cut-off sharply below 80 km as do the nighttime profiles for all vibrational levels. Since these daytime distributions are sensitive to the modes of vibrational quenching, it is suggested that observations of the profiles would be of value in deciding between alternative quenching schemes.

Three-Dimensional Pollutant Modeling in Shear Flow

A steady-state three-dimensional turbulent diffusion equation with variable coefficients describing the concentration distribution of a substance from a point source in a shear flow field is solved analytically. A similar formulation may be developed for line, area, or other kinds of sources. Two models are considered: one treats both the depth and width of the water body as finite, while the other deals with finite depth but with infinite width. In the search for solutions, the integral transformation and the Green’s function constructed earlier by the writer are utilized to the optimum advantage. The solutions are developed for cases in which the velocity and the vertical and lateral eddy diffusion coefficients are given by a power law. Results are compared with those obtained from the uniform flow field. They show a significant difference in the concentration distribution. The magnitude of differences depends on the location of sources and the vertical variations of the velocity and the diffusion coefficients of the flow field.

Use of excess carbon 14 data to calibrate models of stratospheric ozone depletion by supersonic transports

During 1974 at least 7 one-dimensional models of vertical eddy transport and photochemistry had been used to predict the reduction of ozone by nitrogen oxides from supersonic transports. Chang (1974) has shown that these predictions are sensitive to the assumed values for the vertical eddy diffusion coefficient Kz. In this article an effort is made to calibrate the one-dimensional Kz functions against quantitative data for the dissipation of excess carbon 14 from the stratosphere during the period 1963–1970. The data for excess carbon 14, following the nuclear bomb test series of 1961–1962, were published in 1971 and 1972, and these data were not used to derive the various Kz functions. Tables of data are presented in a form that may be useful to others in calibrating two- and three-dimensional models of stratospheric motion. In checking the one-dimensional models the direct observations by balloons at 30°N are primarily used. Also, these data are interpreted as a special hemispherical average (averaging along lines parallel to a standard sloping tropopause). The carbon 14 data and strontium 90 data differ in many important respects, and it is judged that the carbon 14 data give the better estimate of air motion in the stratosphere. The seven Kz models give predictions that strongly differ from one model to another. The models that give a fairly realistic prediction of carbon 14 distribution and persistence are those with minimum Kz between 15 and 20 km and with increasing Kz from 20 to 50 km. Models with these features, as recalculated by Chang (1974), agree with each other as to ozone reduction by artificial nitrogen oxides from supersonic transports (SSTs). These models are used to predict the ozone reduction by SST's according to Grobecker's (1974) upper bound projection out to the year 2025. Very large reductions of global ozone are indicated, more than a factor of 2.

Eddy diffusion in the upper atmosphere by global deposition of meteoroids

A theory for the production of eddy diffusion in the upper atmosphere by the global deposition of meteoroids is presented. It is based on the assumption that meteoroids falling on the Earth carry, on the average, a greater amount of orbital angular momentum per unit mass than that corresponding to the Earth's orbit. This excess of orbital angular momentum of the meteoroids is deposited in some or the other form during their interaction with the Earth's atmosphere. The softer material deposits the excess of its orbital angular momentum in a region slightly higher than the harder material and is held responsible for the superrotation observed in the atmosphere. It is shown that the other population of meteoroids which is metallic in nature deposits the excess orbital angular momentum below 100 km altitude and produces eddies. The size and velocity of the eddies so formed give the value of the vertical eddy diffusion coefficient in agreement with the upper limit set by Johnson and Wilkins (1965) from the study of downward heat transport in the atmosphere.

Stratospheric distributions of odd nitrogen and odd hydrogen in a two-dimensional model

A two-dimensional pole-to-pole chemical model of the stratosphere is developed which extends from 8 to 38 km in altitude. Atmospheric motions are simulated by mean vertical and meridional winds and eddy diffusion coefficients. Seasonally averaged distributions of important odd nitrogen (NO, NO2, and HNO3) and odd hydrogen (H, OH, HO2, H2O2) compounds are computed. Photodissociation of N2O leads to production of odd nitrogen in the stratosphere, and the odd nitrogen is ultimately removed by downward transport into the troposphere and by rain-out (modeled by a rain-out lifetime of 30 days below 8-km altitude). Results are presented for a quasi-steady state in which seasonal cycles repeat themselves. These results show significant latitudinal as well as vertical variations in the predicted species which emphasize the need for at least two dimensions in accurate stratospheric modeling. Computed concentrations are compared with observations when they exist.

Bomb tritium in the Pacific Ocean

During 1959--1973 bomb-produced tritium was monitored in surface seawater from 15 stations in the Pacific Ocean. Some 500 tritium determinations were carried out. Between 1965 and 1972 a series of subsurface samples from 49 locations in the Pacific Ocean was measured, and tritium concentrations as a function of depth were determined. The determinations had a standard error of +- 4% and an uncertainty in the zero value of about 0.17 tritium unit. The most significant oceanographic conclusions that must be drawn from these data can be summarized in the following way: (1) Lateral flow along contours of constant density is the major factor controlling the tritium distribution in the surface and subsurface waters of the Pacific Ocean. Input of tritium into the water below the mixed layer occurs between 45 degree and 30 degree N and south of 60 degree S. The sinking of water in the mid-Pacific at 30 degree N and its flow toward the equator was previously recognized from the presence of a salinity maximum below the thermocline. The southward component of the rate of this flow is estimated to be 1.3+-0.5 cm/s. In many other areas the tritium content of water under the mixed layer ismore » undoubtedly also due to local sinking of surface water and subsequent lateral subsurface flow. (2) An upper limit for the coefficient of vertical eddy diffusion can be calculated. This upper limit of 0.3 cm$sup 2$/s is well below estimates derived by other methods, but it agrees well with the upper limit of 0.2 cm$sup 2$/s derived from tritium measurements in the Sargasso Sea. It appears that transport across lines of constant density is much slower than previously assumed. (3) The mean lifetime of water in the mixed layer of the North Pacific Ocean varies greatly with geographical location. North of 10 degree N the average residence time is between 9 and 15 years, depending on the assumed rate of the molecular exchange of water between atmosphere and ocean. (AIP)« less

Krypton-85 in the Ocean

Abstract A method is described to determine for the first time the 85 Kr concentration in seawater. Samples of 220 l of seawater are degassed aboard a research vessel. The krypton contained in the gas sample is isolated in the laboratory and its 8s Kr activity is measured in a gas counter. The background of the lowel-level counting-array is 0.026 cpm; surface water samples yield a netto count-rate of 0.13 cpm. The reproducibility of the method was checked by gas standards (krypton-air mixtures) and moreover by three surface water samples; both sets agree within ± 1 σ, or ± 5%. The mean value of three samples of great depths (1600, 2000, 2000 m) is 5% of the surface water concentration. This figure represents the possible contamination of the samples by atmospheric 85 Kr during the various preparation stages (blank value). Two profiles have been measured from the North Atlantic (about 40°N, 18°W, November 1972). A strong decrease of the 85 Kr concentration is found in the upper 1000 m. In a simple one-dimensional vertical diffusion-advection model the profiles can be simulated with a coefficient of apparent vertical eddy diffusion of 5 cm 2 / sec in the depth range of 300 to 1000 m (main thermocline). A possible application of oceanic 85 Kr data is the combination of depth profiles with those of other tracers, in particular 3 H. Another application of the 85 Kr method is the dating of groundwaters younger than 20 years.

Entrainment and Diffusion in a Gulf Stream Cyclonic Ring

The mixing and entrainment processes present in a cyclonic ring are investigated by means of a parametric model which is fitted to serial temperature data for a North Atlantic ring. The physical model assumes an axially symmetric ring in which the temperature is presumed to be governed bywhere KA and KZ are the horizontal and vertical eddy diffusivity coefficients and J(ψT) is the (r,z) Jacobian of the transverse streamfunction ψ and the temperature T. Data from two cruises during the 1967 observation of a ring by the Woods Hole Oceanographic Institution provided estimates of the derivatives of the temperature. Regression analysis was used to determine the coefficients for polynomial representations of ψ(r,z) for selected combinations of Kh and Kz. The study indicates upper bounds on the order of magnitude for the diffusivities (Kh,Kz)=(105,10) cm2 s−1 based upon near-minimum least-squares error estimates from the regression analysis. An important result is that little differentiation exists between a purely advective entrainment regime and those regimes including both entrainment and diffusion; i.e., the entrainment circulation appears to be the dominant mechanism in the temporal changes of the ring for a time scale of at least two months. The results provide streamline patterns for the transverse flow from the surface to 1000 m depth consistent with isotherm movement and changes in the ring water masses.

The determination of air-sea exchange and oceanic mixing rates using7Be during the Bomex experiment

The concentrations of 7Be and other radionuclides were measured in air, rain, and seawater in a region east of Barbados, British West Indies, in the summers of 1968 and 1969 during the Barbados Oceanographic and Meteorological Experiment. The radionuclide inventories in the sea varied rapidly owing to the horizontal motion of seawater through the sampling region. The salinity also varied considerably, presumably as a result of Amazon River water carried into the sampling region by the Guiana current, which flows northwestward along the coast of South America. The 103Ru to 95Zr ratio in the top 15 m of the sea indicated that large amounts of these radionuclides from the French nuclear test series at 23°S beginning July 7, 1968, were transported into the sampling region, probably by the Guiana current, on August 15, 1968, and also in June but not in May of 1969. The deposition Of 7Be on the sea surface by rainfall in the sampling region in August 1968 and May through July 1969 was only 13 and 26%, respectively, of that necessary to maintain the measured inventories. it is possible, however, that the inventories resulted from wet deposition outside the sampling region, such as in the intertropical convergence zone, followed by advective transport of the water into the sampling region. The calculated average deposition velocity Of 7Be was 1.0 cm/s, and the calculated average yearly 7Be flux across the sea surface was 1.6×10−2 atom cm−2 s−1. The calculated vertical eddy diffusion coefficient in the sea decreased from greater than 7 cm2/s at the surface to 0.25–0.85 cm2/s at 30–40 m.

Latitudinal distributions of minor neutral hydrogen-oxygen constituents in the winter mesosphere and lower thermosphere

The latitudinal distributions of the concentrations of hydrogen-oxygen constituents are computed in the winter mesosphere and lower thermosphere. Vertical eddy diffusion coefficients varying with latitude and altitude are used, but the effects of horizontal transport are not included. The results show that the distributions of minor constituents have significant latitudinal variations due to the effects of photodissociation and vertical diffusion. It is also indicated that the meridional profile of the O ( 3 P) concentration has a maximum in the latitudes 50°–60° near the mesopause in winter, and that the vertical profile of the O 3 concentration has a second peak near the mesopause, mainly caused by the indirect influences of vertical eddy diffusion. The calculated profiles of the O( 3 P) and O 3 concentrations, the atomic-to-molecular oxygen concentration ratios, and airglow emission rates are compared with the recent available observations, showing fairly good agreement. Comparison of the theoretical O( 3 P) concentrations and 5577 Å airglow emissions suggests an important role of horizontal transport in the lower thermosphere.

Jovian Atmosphere: Structure and Composition between the Turbopause and the Mesopause

The occultation of the star Beta Scorpii by Jupiter was observed at high time resolution in three wavelength channels. The results imply a temperature of 220 degrees K at an altitude in the Jovian atmosphere corresponding to 10(14) molecules per cubic centimeter, and temperature fluctuations of 2 degrees to 10 degrees K over vertical scales of 2 to 10 kilometers. They suggest that the vertical eddy diffusion coefficient near the turbopause has a lower limit of 7 x 10(5)K square centimeters per second, and that the turbopause lies above the altitude where the density is 5 x 10(13) molecules per cubic centimeter. Below the turbopause, the ratio of hydrogen to helium is consistent with cosmic abundances.

The estimation of vertical eddy diffusivities below the thermocline in lakes

Mathematical models of the spatial and temporal variation of passive substances in lakes and oceans require a quantitative formulation of vertical turbulent transport. Methods of estimating vertical eddy diffusivity coefficients in lakes for such substances as temperature, inorganic ions, or biologically active materials are briefly reviewed. One widely used method, the McEwen method, is discussed, and it is shown how this method can lead to erroneous results. Another method, the flux gradient method, is examined and compared with the McEwen method in specific case studies of thermal energy transfers. Lack of agreement between values obtained by the McEwen method and the flux gradient method has led some investigators to postulate‐a flux of thermal energy into the deep layers of a lake by density currents. An alternative explanation of the discrepancy is offered by noting that deepwater turbulent mixing may result from a microstructure of layers and sheets caused by, for example, a Kelvin‐Helmholtz shear instability in the flows or other instability mechanisms.

Vertical Exchange Measurements in the Lower Troposphere Using ThB (Pb-212) and Radon (Ru-222)

Abstract Various methods of determining vertical eddy diffusion coefficients in the planetary boundary layer from two natural radioactive tracers, radon (Rn-222) and ThB (Pb-212), are presented and discussed. In all cases, it is more pertinent to measure vertical exchanges in the lower atmosphere using ThB (10.6 hr half-life) than radon (3.8 days half-life). About 30 vertical profiles of Rn and ThB in the lower troposphere (100–3000 m) are determined over a 12-month period. Vertical eddy coefficient values are calculated according to the various methods discussed. The variation range, between 10−1 and several 100 m2 sec−1, is large and closely related to the vertical temperature gradient variation. Low values (10−2 to 10−1 m2 sec−1) of the exchange coefficients determined in the inversion layer which frequently exists at the top of the planetary boundary layer show that vertical turbulent fluxes toward the free atmosphere are relatively small.

Vertical Eddy Diffusion Studies in the Thermocline of a Small Stratified Lake

Values for K, the coefficient of vertical eddy diffusion in the thermocline of lake 227, a small, highly stratified, and artificially eutrophied lake in northwestern Ontario, Canada, are presented. Three methods: the classical temperature method of McEwen, a dye method, and a new method using a RAGAPOS (Radon Gas Point Source), were used. Results ranged from 2 × 10−4 cm2/sec by the Rn method to 34 ×10−4 cm2/sec by temperature method; the dye method resulted in an average value of 12 × 10−4 cm2/sec. The recycling of ΣCO2 resulting from particulate degradation below the epilimnion was calculated. The results ranged from 8 to 53% of the net loss of carbon from the empilinion depending on the K value used. Results from the radon method are considered to be more accurate than results from the temperature method.

Some physicochemical features of a meromictic Lake Suigetsu

Physicochemical features of a typically meromictic lake, Lake Suigetsu, are studied. Vertical distributions of temperature and chlorinity show that the lake is well stratified, and no marked mixing occurs between the upper fresh water and lower salt water. In the chemocline, the vertical gradient of density is large, and the vertical eddy diffusion coefficient is as low as 1.5 × 10−2 cm2 sec.−1 Dissolved oxygen is saturated in the surface portion of the upper water, and then rapidly decreases with depth towards the chemocline, where sulfide first appears and increases towards the bottom. In the chemocline oxygen consumption is prominent process reaching 290 mg 02/m2/day. The oxidation of sulfide, supplied from the underlying water layer, is the main factor causing the oxygen consumption in the chemocline.

Vertical eddy diffusion coefficient in Lake Zürich

The vertical eddy diffusion coefficient in Lake Zurich is a strong function of both depth and season. In the deep lake, the annual oxygen consumptions by the oxidation of organic carbon is balanced out by the equal amount of oxygen supply from above by diffusion.

Measurements of the equatorial undercurrent in the eastern Pacific

During the Piquero Expidition (June 26–August 4, 1969) direct measurements of the Pacific Equatorial Undercurrent were made at four longitudes between 115.5° and 93.5°W. Eastward volume transports of the Undercurrent were 19 × 10 6 m 3 sec −1 at 115.5°W and 8 × 10 6 m 3 sec −1 at 93.5°W. Transports of the South Equatorial Current and the Undercurrent were comparable to those measured on Swansong (September–November 1961). Comparison of the Swansong and Piquero measurements with those of Dolphin (April–May 1958) and Eastropac (April 1968) suggests that the Undercurrent transport is less when the southeast trade winds and the South Equatorial Current are strongest. Measurements east of 118°W on all expeditions show higher velocities to the south of the equator than the north. This asymmetry may be due to the southerly component of wind at the equator in the eastern Pacific. Beneath the Undercurrent there was a secondary maximum of east flow at the base of the thermostad; speeds ranged between 12 and 34 cm sec −1 and the thermosteric anomaly at the maximum was near 160 cl ton −1. At 115.5°W there was a divergence in meridional transport in the surface layer (upper 28 m). The magnitude of the integrated poleward transport was approximately equal to the poleward Ekman transport given by the zonal wind stress component. In order to satisfy continuity of mass upwelling of water into the surface layer was required. The computed vertical velocity component is 8 × 10 −3 cm sec −1. Current measurementsat the depth of the Undercurrent did not indicate equator-ward flow towards the equator. This is in contrast to the Swansong results. Slopes of the pressure surfaces relative to 500 db indicate that there was no mean zonal pressure force east of 115.5°W. Computation of the longitudinal distribution of maximum east current of the Undercurrent with a simple model indicates that frictional dissipation may be important west of the Galápagos Islands. Low-salinity and high-salinity cores were found north and south of the equator at 115.5°W. The high-salinity core was present west of the Galápagos Islands but the low-salinity core was absent. The high-salinity core was located at the depth of maximum Väisälä frequency. Computation of the coefficient of vertical eddy diffusion of salt gave a value of 4 × 10 −2 cm 2 sec −1.