Vertical Temperature Variations Research Articles

Hypolimnetic density currents traced by sulphur hexafluoride (SF6)

The artificial tracer sulphur hexafluoride (SF6) has been used to study the density-driven deep water exchange between two sill-separated basins of Lake Lucerne, Gersauersee and Urnersee. The sources of the density gradients between the two basins are (1) salinity differences between the major inlets due to the different geology of their drainage areas, and (2) temperature differences due to spatial variation of wind forcing. Wind speeds are generally larger in Urnersee, especially in spring during the so-called Föhn events, when winds blow from the south. In contrast, Gersauersee is protected form these winds. In spring 1989, a total of 630 g of SF6 was released at 80 to 120 m depth in the small Treib Basin located between Urnersee and Gersauersee. During about 100 days the distribution of SF6 in the lake was determined by gaschromatography. Two models are used to quantify the exchange flow, (1) a one-box mass balance model for SF6 in the deep part of Treib Basin, and (2) a one-dimensional diffusion/advection model describing the temporal and vertical temperature variation in Urnersee. According to the first model, the flow into the deep hypolimnion of Urnersee, decreases from 21·106 m3·d−1 at the end of March to about 8·106 m3·d−1 in late April. The second model yields similar flow rates. The decrease of the flow rate during spring, confirmed by both approaches, is consistent (1) with the decreasing strength of the density gradient above the sill during spring and early summer, and (2) with hydrographic information collected in Lake Lucerne during other years.

Hypolimnetic density currents traced by sulphur hexafluoride (SF6)

The artificial tracer sulphur hexafluoride (SF6) has been used to study the density-driven deep water exchange between two sill-separated basins of Lake Lucerne, Gersauersee and Urnersee. The sources of the density gradients between the two basins are (1) salinity differences between the major inlets due to the different geology of their drainage areas, and (2) temperature differences due to spatial variation of wind forcing. Wind speeds are generally larger in Urnersee, especially in spring during the so-called Fohn events, when winds blow from the south. In contrast, Gersauersee is protected form these winds. In spring 1989, a total of 630 g of SF6 was released at 80 to 120 m depth in the small Treib Basin located between Urnersee and Gersauersee. During about 100 days the distribution of SF6 in the lake was determined by gaschromatography. Two models are used to quantify the exchange flow, (1) a one-box mass balance model for SF6 in the deep part of Treib Basin, and (2) a one-dimensional diffusion/advection model describing the temporal and vertical temperature variation in Urnersee. According to the first model, the flow into the deep hypolimnion of Urnersee, decreases from 21·106 m3·d−1 at the end of March to about 8·106 m3·d−1 in late April. The second model yields similar flow rates. The decrease of the flow rate during spring, confirmed by both approaches, is consistent (1) with the decreasing strength of the density gradient above the sill during spring and early summer, and (2) with hydrographic information collected in Lake Lucerne during other years.

Chaos theory, psychiatry, and a quiet revolution

What is probably one of the most exciting potential advances in psychiatry is occurring slowly, possibly too slowly and has gone unnoticed by many. I am talking about ‘Chaos theory’, which is a mathematical concept that has influenced the study of such diverse subjects as the weather, evolution and the electroencephalogram. Is it our lack of mathematical training that makes us so fearful? This may be so, but we can still understand chaos theory without having to learn large mathematical formulae.Chaos theory is about dynamic non-linear systems that are orderly at first, but may become completely disorganised over time. That is initial conditions that are alike in the beginning, may have markedly different outcomes over time. An analogy commonly drawn from weather studies is the butterfly effect. This draws on the premise of initial conditions which is a butterfly fluttering its wings in Tokyo can lead over time and distance to a storm for example over New York. In other words a small perturbation in a non-linear system can lead to great variations in outcome. The chaos theory is about how phenomena can vary between different kinds of states around what is called a ‘strange attractor’ and obtain from this a semblance of order out of what initially can be perceived as disorder.In this way chaos differs from random behaviour and causal systems. Eventual outcome in a random system is not determined by initial conditions. The eventual outcome in a causal system has a linear relationship with its initial conditions. In other words a small change in initial conditions will lead to a small change in the eventual outcome. But in Chaos theory a small change in the initial conditions can lead to major changes in the eventual outcome. These changes become exponential over time.The original example of a chaotic system was developed by Lorenz. In his early work on weather systems he found using computer simulations that started with similar, but slightly different initial data, orbits would stay close to each other for a while but would eventually diverged in a manner that turned out to be exponential over time. His model was deterministic, that is the orbits were unique in the sense that there was only one orbit passing through a given point of the space in which the orbit lay. The three variables he was measuring were convective air circulation in relation to vertical and horizontal temperature variations.

Hypolimnetic density currents traced by sulphur hexafluoride (SF

The artificial tracer sulphur hexafluoride (SF6) has been used to study the density-driven deep water exchange between two sill-separated basins of Lake Lucerne, Gersauersee and Urnersee. The sources of the density gradients between the two basins are (1) salinity differences between the major inlets due to the different geology of their drainage areas, and (2) temperature differences due to spatial variation of wind forcing. Wind speeds are generally larger in Urnersee, especially in spring during the so-called Fohn events, when winds blow from the south. In contrast, Gersauersee is protected form these winds. In spring 1989, a total of 630 g of SF6 was released at 80 to 120 m depth in the small Treib Basin located between Urnersee and Gersauersee. During about 100 days the distribution of SF6 in the lake was determined by gaschromatography. Two models are used to quantify the exchange flow, (1) a one-box mass balance model for SF6 in the deep part of Treib Basin, and (2) a one-dimensional diffusion/advection model describing the temporal and vertical temperature variation in Urnersee. According to the first model, the flow into the deep hypolimnion of Urnersee, decreases from 21·106 m3·d−1 at the end of March to about 8·106 m3·d−1 in late April. The second model yields similar flow rates. The decrease of the flow rate during spring, confirmed by both approaches, is consistent (1) with the decreasing strength of the density gradient above the sill during spring and early summer, and (2) with hydrographic information collected in Lake Lucerne during other years.

Estimation of permafrost thickness using ground geophysical measurements, and its usage for defining vertical temperature variations in continental ice and underlying bedrock

Abstract In bedlock covered by continental ice, the depth to electrically conductive saline waters enriched below permafrost can be defined by electromagnetic measurements. Thus, if the ice thickness is also measured we obtain estimates of permafrost thickness variations in the survey area. Moreover, using the relation between ice and permafrost thicknesses and approximations of the melting temperature of saline waters combined with the average annual temperature at the surface, we can estimate temperature variations within both the bedrock and the ice. These can further be used for estimating the temperature values at the ice base. The method was developed for interpreting two geophysical field profiles measured on continental ice in western Dronning Maud Land, Antarctica. Gravity, magnetic and electromagnetic profiles were measured between the nunataks Basen and Plogen (≈22 km) and Basen and Fossilryggen (≈38km). In the Basen–Fossilryggen profile the electromagnetic soundings revealed good conductors in the bedrock beneath the ice. The significant correlation between the ice thickness and the depth of the conductor in the bedrock strongly suggests that the conductors are not sedimentary rock layers but rather saline groundwater in which salinity has been enhanced by permafrost processes. From the regression curve we can conclude that the temperature vs depth curve in the ice can be represented by a first-degree line and that the “warm” ice base of about −2° C is expected to occur at depths of about 650 m, the base of permafrost in outcropping bedrock being at about 1 km. The mean temperature gradients in the ice and in the bedrock can be estimated as being about 20°Ckm−1 and 13°C km−1 respectively. In the Basen–Plogen profile, conductors were detected only in the beginning of the profile, where ice thickness was below 650m. In the main part of the profile where the ice thickness exceeds 650 m, no conductors were observed. In those areas our interpretation is that the icebase is “warm” and no saline waters enriched by permafrost are present.

Estimation of permafrost thickness using ground geophysical measurements, and its usage for defining vertical temperature variations in continental ice and underlying bedrock

AbstractIn bedlock covered by continental ice, the depth to electrically conductive saline waters enriched below permafrost can be defined by electromagnetic measurements. Thus, if the ice thickness is also measured we obtain estimates of permafrost thickness variations in the survey area. Moreover, using the relation between ice and permafrost thicknesses and approximations of the melting temperature of saline waters combined with the average annual temperature at the surface, we can estimate temperature variations within both the bedrock and the ice. These can further be used for estimating the temperature values at the ice base.The method was developed for interpreting two geophysical field profiles measured on continental ice in western Dronning Maud Land, Antarctica. Gravity, magnetic and electromagnetic profiles were measured between the nunataks Basen and Plogen (≈22 km) and Basen and Fossilryggen (≈38km). In the Basen–Fossilryggen profile the electromagnetic soundings revealed good conductors in the bedrock beneath the ice. The significant correlation between the ice thickness and the depth of the conductor in the bedrock strongly suggests that the conductors are not sedimentary rock layers but rather saline groundwater in which salinity has been enhanced by permafrost processes. From the regression curve we can conclude that the temperature vs depth curve in the ice can be represented by a first-degree line and that the “warm” ice base of about −2° C is expected to occur at depths of about 650 m, the base of permafrost in outcropping bedrock being at about 1 km. The mean temperature gradients in the ice and in the bedrock can be estimated as being about 20°Ckm−1 and 13°C km−1 respectively.In the Basen–Plogen profile, conductors were detected only in the beginning of the profile, where ice thickness was below 650m. In the main part of the profile where the ice thickness exceeds 650 m, no conductors were observed. In those areas our interpretation is that the icebase is “warm” and no saline waters enriched by permafrost are present.

Deductions from a simple climate model: Factors governing surface temperature and atmospheric thermal structure

Radiative equilibrium solutions are the starting point in our attempt to understand how the atmospheric composition governs the surface and atmospheric temperatures, and the greenhouse effect. The Schwarzschild analytical grey gas model (SGM) was the workhorse of such attempts. However, the solutions suffered from serious deficiencies when applied to Earth's atmosphere and were abandoned about 3 decades ago in favor of more sophisticated computer models. Here we show that simple heuristic modifications to the SGM resolve these deficiencies, at least the catastrophic ones. The modifications include the addition of a spectral window, as well as allowing the scale height of optical depth to be different from that of the atmospheric pressure. The modified SGM reveals the fundamental factors that govern the radiative equilibrium thermal structure. (1) The presence of a spectral window allows the temperature jump between the surface and the immediately overlying atmosphere to become small, irrespective of the magnitude of the surface temperature. (2) In an optically thick atmosphere (such as Earth and Venus), the surface temperature and the runaway greenhouse effect depend inversely (as the one‐fourth power) on the Planck function‐weighted width of the window and are independent of the optical depth and other atmospheric parameters. The vertical variation of temperature within the atmosphere, however, is determined by the vertical variation of optical depth. (3) The degree of convective instability of the radiative equilibrium thermal structure γ is proportional to the ratio H/Hτ, where H is the atmospheric scale height and Hτ is the scale height of the vertical variation of optical depth. Here, γ is the ratio of the radiative equilibrium lapse rate and the neutral lapse rate for dry convection; γ > 1 indicates that the profile is unstable to free convection. Thus Hτ < H emerges as one of the fundamental criteria for convective instability. These factors lead to several corollaries regarding the specific details of atmospheric thermal structure on Earth and Venus. For example, according to the modified SGM, the radiative equilibrium temperature profile is strongly superadiabatic in Earth's lower atmosphere because Hτ is dominated by the water vapor's scale height being much less (2 compared with 8 km) than the atmospheric scale height. In the case of Venus, the pressure broadening of the CO2 rotational lines makes Hτ a factor of 2 smaller than H. Some of these results have been obtained using more detailed, multispectral radiative equilibrium models.

Ray tracing in a moving medium with two-dimensional sound-speed variation and application to sound propagation over terrain discontinuities

The development of an efficient method for tracing rays and determining sound pressure levels in a moving medium is described. The medium is specified with horizontal and vertical variations in temperature and vectorial wind velocity. Reflections from a nonlevel ground surface of complex impedance are treated and an adaptive time step numerical integration is implemented for high accuracy. Two integration algorithms are compared for accuracy and computational efficiency. Recommendations are given for improved discretization of the medium and for accurate ray tracing through a ground reflection. This model is used to investigate the effect that terrain discontinuities, such as hills, have on atmospheric sound propagation. The importance of correct inclusion of the vectorial nature of wind is demonstrated.

Analytical Solution for Two‐Dimensional Heat Conduction beneath a Partial Surface Mulch

AbstractModels describing heat conduction in materials subjected to periodically varying surface temperatures are important in agricultural physics and other disciplines of applied physics. To date, most attempts to model soil heat conduction in two dimensions have relied on methods of numerical approximation to solve the heat‐conduction equation. We have developed an exact analytical solution to the heat‐conduction equation in a two‐dimensional region of constant thermal properties. The surface temperature is described by a wave that varies sinusoidally with time and that has mean temperature, amplitude, and phase constant as arbitrary functions of space. In addition to a general solution, a particular solution is presented for a surface temperature pattern corresponding to a partial surface mulch. Calculated temperature and heat‐flux profiles beneath a partial surface mulch indicate that, at certain times of the day, there are large vertical and horizontal spatial variations in temperature and heat flux but, at other times, temperatures are uniform and heat fluxes have similar magnitude and direction. The calculations also show that, near the soil surface, the horizontal component of the heat flux can be quite large.

NONDESTRUCTIVE EVALUATION METHOD OF CONCRETE PAVEMENT BY FWD

Nondestructive evaluation method of concrete pavement using deflections measured by a Falling Weight Deflectometer (FWD), has been developed. In this procedure, the mechanical properties of a concrete slab and foundation can be obtained by backcalculating from the FWD deflections measured at the slab center. Load transfer efficiency at a joint can be quantified from the FWD deflections measured at the joint. Furthermore, a void beneath the concrete slab can be detected and its size can be estimated. The time when the FWD measurement should be conducted is specified to minimize the influence of a vertical variation of temperature in a concrete slab.

Automatic cross-wall temperature monitor for coke ovens

A system has been devised for the automatic measurement of the temperature of coke as it is ejected from an oven following carbonisation. It gives information on both the vertical and longitudinal temperature variations within the oven, and the measurements can be related to the positions of individual flues within the heating walls.

Stratospheric cloud micro‐layers and small‐scale temperature variations in the Arctic in 1989

Thin layers of large (r ≈ 2–3 μm) particles were observed in the Arctic between 14 and 27 km on 23 and 30 January 1989. Although the particle mass is consistent with the available HNO3 vapor, it is not always clear whether the morphology of the layers is the result of recent condensation or evaporation as the layers appear under conditions of both supersaluration and undersaturation with respect to nitric acid trihydrate (NAT). Large amplitude, small vertical scale temperature variations appear to be associated with the layers but not in a simple manner. In regions supersaturated with respect to NAT, condensation on only a few of the available condensation nuclei takes place. Such preferential condensation into thin large particle layers suggests that this class of nuclei may be different than the previously assumed sulfate aerosol nuclei. The possibility that they may be derived from solid fuel rocket effluent and spacecraft ablation products is examined and cannot be excluded. Such a source may explain the appearance of these cloud layers at high altitude.

Tomographic Imaging as a Tool for Reservoir Surveillance and Developmental Geology: ABSTRACT

Tomographic image reconstruction techniques are being successfully extended for use in high resolution imaging of hydrocarbon reservoirs. Important applications of this technology include monitoring the movement of fluids in enhanced oil recovery (EOR) projects and analysis of reservoir structure, lithology, and mechanics. Typically, data is acquired between boreholes (cross-borehole tomography) or between borehole and surface (tomographic vertical seismic profile (VSP) and inverted VSP). By recording multiple components of the wave field, shear, and compressional wave velocity, tomograms can be reconstructed. From these images, additional tomograms of various elastic moduli of the reservoir rock can also be reconstructed, including bulk modulus (incompressibility), shear modulus, and Poisson's ratio. These tomograms carry information about lateral and vertical variations in reservoir lithology, fluid content, pressure, and temperature. Attention is now being focused on the interpretation of tomograms and the relationship between rock properties and geophysical measurements. The successful application of this technology to reservoir surveillance should result in improved field development and more efficient EOR programs.

Observations of small eddies in the Beaufort Sea

The horizontal and vertical variations of velocity, temperature, density, and turbulent kinetic energy dissipation in the central Beaufort Sea were measured with helicopter‐borne expendable current profilers and conductivity‐temperature‐depth units. Almost all velocity differences larger than 0.05 m s−1 could be consistently interpreted as being due to nearly circular eddies with a diameter of 10–20km, a thickness of 50–500 m, peak velocities of 0.07–0.3 m s−1, and little expression at the top of the ocean. Four such eddies were found. Two anticyclones were found and accurately sampled. Two cyclones were found but were only poorly sampled; both were beneath and close to one of the anticyclones. Relative vorticity could be computed for two anticyclones and one cyclone. Within experimental error, the two anticyclones, and all historical Beaufort Sea anticyclones, had a relative vorticity of −ƒ and thus zero potential vorticity at the center. The cyclone had a central relative vorticity of about 0.5ƒ and thus a different value of potential vorticity than the surrounding fluid. One anticyclonic eddy (B) was sampled seven times over a period of 23 days. Its measured velocity and density fields were in approximate gradient wind balance. Its central core contained values of temperature, nitrate, and silicate that were different from those outside the core at the same density. It moved eastward at about 0.02 m s−1 through the surrounding fluid. Measurements of turbulent kinetic energy dissipation were almost always less than the noise level of the instrument (about 10−9 W kg−1), corresponding to a mean dissipation much less than this and a minimum decay time due to turbulence much longer than 0.3 year. The nondimensional strength (Rossby number) and shape (Burger number) of anticylcone B are very similar to those of other Beaufort Sea anticyclones and similar to those of small mid‐latitude eddies. Each of the eddies observed here was centered on a temperature maximum associated with one of the warm water masses that advect into the Arctic Ocean. The two anticyclones were centered on temperature maxima originating in the Pacific Ocean, whereas the two cyclones were centered on temperature maxima from the Atlantic Ocean. This is consistent with the hypothesis that the eddies are formed as these water masses enter the Arctic Ocean.

A numerical model for the formation of saline waters due to diffusion of dissolved NaCl in subsiding sedimentary basins with evaporites

Numerical modeling by a finite difference method incorporating the effects of vertical variations in pressure, temperature, salinity, and porosity shows that mass transport by diffusion may be a major brine-forming process in sedimentary basins containing halite beds. Vertical fluxes of dissolved NaCl are greatest when the subsidence rate is slow. At subsidence rates of 20 m m.y. −1 more than 250 m of salt can be dissolved over 150 m.y. At rapid subsidence rates, such as 500 m m.y. −1, pore waters are advected downward so rapidly that although a diffusion front develops above the evaporite, this front moves downward as the evaporite subsides, and diffusive fluxes at shallow depths are thus low. However, under such conditions, the pore water column becomes gravitationally unstable as a result of thermally-induced density inversions and the potential for convective overturn is enhanced with accompanying advective salt flux upward. Although dissolution and diffusion of NaCl are important processes in the burial history of evaporites, they are not adequate by themselves to produce the regional salinity versus depth profiles that are actually observed in some sedimentary basins. Diffusion-induced gradients progressively increase with depth whereas gradients actually observed in sedimentary basins tend to decrease with depth. The difference is presumably due to the activity of other mass transport mechanisms such as advection, convection and dispersion.

A Theoretical Method for Computing Vertical Distributions of Acidity and Sulfate Production within Cumulus Clouds

Abstract An aqueous chemistry model has been combined with an entraining cumulus cloud model to predict vertical distributions of pH (=−log10[H+]) within a cloud. The cloud model predicts vertical variations of temperature, pressure, entrainment and liquid water content. The aqueous chemistry model incorporates the effects of soluble aerosols, trace gases and aqueous-phase SO2 oxidation on cloudwater pH levels. In the absence of SO2 oxidation, vertical distributions of pH were found to be highly variable, depending on several chemical and meteorological factors. For clouds forming in an environment where the aqueous composition is determined primarily by dissolved sulfate condensation aerosol, pH was found to increase with height above cloud base primarily due to dilution by increasing water content. If cloudwater acidity levels are predominantly determined by dissolved SO2, HNO3 and formic acid gas, pH variations with height were not so clearly defined, with the diluting effects of entrainment, liquid wa...

COUPLING A ONE-DIMENSIONAL MODEL FOR SIMULATING RUN–OF–THE–RIVER RESERVOIRS

ABSTRACT A mathematical model of Lake Ashtabula Reservoir, Valley City, N. Dak., was developed based on the one-dimensional reservoir thermal model, CE-THERM-R1. The major assumption employed in CE-THERM-R1 is that the reservoir is represented as a vertical series of completely mixed horizontal layers (one-dimensional assumption). Longitudinal and lateral variations of constituent concentrations cannot be predicted. Lake Ashtabula, whose pool is long, narrow and largely confined to the run-of-the-river, exhibits both vertical and longitudinal water quality gradients. To represent this two-dimensional aspect of the system, the model was organized using three CE-THERM-R1 pools coupled in series in which the simulated outflow constituent quantities for the first and second pools became the inflows for their respective downstream pools. By using this model configuration it was possible to simulate longitudinal as well as vertical temperature variation and the concentration of total dissolved solids, thus reducing the severity of the one-dimensional assumption.

The stability of buoyancy-driven rolls aligned with a shear flow when the temperature gradient is nonlinear

The buoyancy driven instability of rolls aligned with a shear flow of a Boussinesq fluid is considered. It is supposed that the temperature varies not only with height but also in the direction of the flow thus allowing the vertical temperature profile to be nonlinear. Conditions are derived for the neglect of the horizontal temperature gradient in the perturbation equations. These are (i) that the vertical temperature gradient varies sufficiently slowly in the direction of the flow and (ii) that Pr h/d≫1, where Pr is the Prandtl number and h and d are the length scales for the vertical variation of velocity and temperature, respectively. Under these conditions, stability is governed by the equation for Bénard convection. The principle of exchange of stabilities is proved for an arbitrary temperature gradient profile, with isothermal, free-surface boundary conditions, and the equation is solved numerically and by an asymptotic method for a model thermal boundary layer. The analysis is then applied to an experimental study of spoke patterns, observed in the growth of electronic materials. This work also indicates that a previous investigation of the stability of stratified shear flow has a restricted range of validity.

Determination of the vertical neutral temperature and wind profiles using EISCAT and HF Doppler radar

Simultaneous observations by EISCAT and an HF Doppler system of a TID are presented. Crossspectral analysis of the data allows the vertical variation of the neutral temperature and horizontal wind in the thermosphere to be determined.

Lake—Wide Seasonal Changes in Limnological Conditions in Lake Michigan in 1976

Data collected on lake-wide cruises in 1976 were used to study seasonal and vertical variations in water temperature, transparency, chlorophyll a, and nutrients in Lake Michigan. Data were analyzed according to subsets corresponding to the northern and southern open lake. Comparisons (t-tests) of data from the open lake indicated that the average water temperature was cooler and average water transparency was greater in the northern lake than in the southern, but with the exception of total phosphorus, average nutrient concentrations did not differ between the northern and southern parts. It was found that physical-chemical characteristics of nearshore and Straits of Mackinac stations differed significantly from open lake stations. Seasonal phytoplankton dynamics in the open lake were related to seasonal and vertical changes in silica and nitrate nitrogen. The spring phytoplankton bloom occurred before the lake was strongly stratified thermally. After thermal stratification was well developed, epilimnetic concentrations of chlorophyll a decreased, probably due to some combination of nutrient limitation and zooplankton grazing, and maximum chlorophyll a concentrations were found below the thermocline. Epilimnetic silica concentrations decreased after thermal stratification and diatoms were replaced in the phytoplankton assemblage by green and blue-green algae in late summer. Total phosphorus averaged only 8 μg/L on a lake-wide basis and thus only small but significant reductions in absolute concentration can be expected from phosphorus control programs. However, over a period of several years, these small reductions in concentration may be difficult to verify from total phosphorus measurements which have relatively large sampling errors and variances.