Mean Potential Temperature Research Articles

The Explicit Planetary Isentropic-Coordinate (EPIC) Atmospheric Model

We describe a new general circulation model (GCM) designed for planetary atmospheric studies called the EPIC model. This is a finite-difference model based on the isentropic-coordinate scheme of Hsu and Arakawa (1990.Mon. Wea. Rev.118, 1933–1959). We report on previously undocumented modifications, additions, and key practical issues that experience running the model has revealed to be important. The model integrates the hydrostatic primitive equations, which are valid for large-scale atmospheric dynamics and include gravity waves (buoyancy waves), planetary waves (Rossby waves), and horizontally propagating sound waves (Lamb waves), but not vertically propagating sound waves because of the hydrostatic approximation. The vertical coordinate is entropy in the form of potential temperature, which coincides with material surfaces for adiabatic motion. This means that there is no vertical velocity except where there is heating, which improves accuracy and helps the model maintain conservation properties over long integrations. An isentropic vertical coordinate is natural for the atmospheres of Jupiter, Saturn, Uranus, and Neptune, which are believed to have essentially adiabatic interiors that match up with the bottom of the model and is also excellent for middle-atmosphere studies on any planet. Radiative processes are parameterized by Newtonian cooling, and the latent heat of ortho–para hydrogen conversion is included when appropriate, with a suitably defined mean potential temperature. The model is written with general map factors that make it easy to configure in oblate spherical, cylindrical, or Cartesian coordinates. The code includes optional Message Passing Interface (MPI) library calls and hence runs on any Unix-based parallel computer or network cluster. An optional graphical user interface to commercial visualization software facilitates control of the model and analysis of output. Memory is allocated dynamically such that the user does not recompile to change horizontal or vertical resolution or range. Applications to date include comet impact forecasts and hindcasts for Jupiter, meridional circulation studies of Uranus and Neptune, and the accompanying paper on three-dimensional simulations of Neptune's Great Dark Spot (1998.Icarus132, 239–265).

Energy dissipation rates, eddy diffusivity, and the Prandtl number: An in situ experimental approach and its consequences on radar estimate of turbulent parameters

Different methods have been proposed to derive the energy dissipation rate and eddy diffusion coefficients from ST radar measurements. However, their validity is still questionable because they implicitly assume that the Prandtl number is always equal to one, an assumption which is not verified. An experimental approach to this question, using balloon‐borne experiment results, is proposed in this paper in order to test the validity/invalidity of the methods generally used. In situ observations show that the potential temperature gradient is more efficiently (and probably more rapidly) eroded by the turbulent activity than the wind shear. As a consequence of this observational evidence already mentioned by Browning and Watkins [1970], the structure function constant for temperature fluctuations (CT2) is vanishing within fully developed turbulent layers and exibits maxima on their boundaries, while the structure parameter for wind fluctuations (CV2) presents a broad maximum within the same layer and is decreasing at its boundaries. Consequently, the gradient Richardson number Ri strongly varies within fully developed turbulent layers, from Ri close to zero (near their center) up to Ri >1 (at their boundaries). By contrast, the flux Richardson number Rf, which describes the evolution of the ratio between buoyancy flux and turbulent energy production, remains apparently quasi‐constant and close to its critical value during the erosion processes, so that the Prandtl number is not a constant close to unity but might also strongly vary during the turbulent life cycle. These results are in good agreement with laboratory experiments in statistically stable fluids reviewed by Thorpe [1973] and with experimental results obtained in the boundary layer [Businger et al., 1971; Gossard and Frisch, 1987]. ST radar are generally not able to observe regions where the potential temperature gradient is eroded by the turbulent activity but may obtain strong responses on the boundaries of fully developed turbulent layers. This behavior does not affect the radar capability of estimating eddy dissipation rate ϵ and eddy diffusivity Kθ (or KM) when complementary information on temperature profiles and humidity are available. It is shown that the “nonlocal” mean potential temperature gradient, the wind shear, and the flux Richardson number are the pertinent parameters allowing a correct estimate of the eddy dissipation rates and eddy diffusion coefficients, from Cn2 (CT2) and rms turbulent vertical wind, in regions where the turbulent activity is observable by ST radars.

Calculation of the global land surface energy, water and CO2 fluxes with an off‐line version of SiB2

Global land surface fluxes of energy and CO2 have been simulated using an off‐line version of a biosphere‐atmosphere model, SiB2, forced with analyzed or observed atmospheric boundary layer mean potential temperature, water vapor mixing ratio, and wind, surface downward solar and thermal radiation, and precipitation. The off‐line model is called SiBDRV. Soil and vegetation boundary conditions were specified from satellite data and other sources. The European Centre for Medium‐Range Weather Forecasts (ECMWF) data assimilation system products were used to derive the atmospheric and radiative forcings. Precipitation was based on station observations. The SiBDRV results were compared with corresponding simulation results produced by the Colorado State University general circulation model (CSU GCM), with the ECMWF assimilation system output and with observations. Differences between the surface energy budget components and the surface climatology produced by SiBDRV and the ECMWF assimilation system are due to differences in the land surface parameterizations between the two models. SiBDRV produced lower surface latent heat fluxes and larger sensible heat fluxes than the ECMWF data assimilation, partly due to large canopy resistent term explicitly formulated by SiB2 and possible precipitation differences between the SiBDRV precipitation forcing and the ECMWF data. Differences between the SiBDRV and the CSU GCM results are due to the different climates associated with the ECMWF assimilation system output, which is strongly constrained by assimilated observations, and by the CSU GCM, which is run in pure simulation mode. More specifically, the major reasons for the surface energy and CO2 budget differences between the SiBDRV and the GCM are greater incoming solar radiation in the GCM and differences in the precipitation patterns. The simulated global annual carbon uptake by the terrestrial biosphere is similar in SiBDRV and the GCM. The annual gross primary productions of SiBDRV (116 Gt) and the GCM (113 Gt) agree well with other studies, using either ecological process models or empirical regression models. SiBDRV takes up 10 and 5% more CO2 than the GCM in January and July, respectively. The seasonally varying land surface CO2 fluxes estimated by the SiBDRV and the GCM both compare reasonably well with the results of other calculations.

The Source Regions of Ocean Island Basalts

The geochemical modelling of many small-volume continental magmas shows that their source regions must have been depleted by basalt formation, and later enriched by the addition of a metasomatic melt, formed by melting ∽0·3% of the MORB source. The presence of such magmas throughout western Turkey and the Aegean, where no plume is present, requires such magmas to be formed at temperatures considerably below the dry solidus. Similar magmas elsewhere bring up nodule suites, many of which have the same composition as the source regions of the host magmas. Pressure and temperature estimates from garnetbearing suites, and temperature estimates from those without garnet, show that the nodules last equilibrated at pressures and temperatures close to those of the wet solidus. Magmas from the smaller oceanic islands and from some seamounts closely resemble small-volume continental magmas, and also come from sources that have been metasomaticaUy enriched. However, no data sets from any of the oceanic islands that have yet been modelled require their source regions to have been depleted before being enriched The density of the sources of continental and oceanic basalts can be obtained from their calculated modes. In the garnet peridotite stability field the sources of ocean island basalts have densities that are slightly greater than that of the MORB source, whereas those of most small-volume continental magmas are lighter. Therefore ocean island sources alone are easily entrained into the thermal convection beneath the plates. A numerical experiment shows that material in the hot and cold boundary layers of high Rayleigh number time-dependent convection tends to remain in the boundary layers for several overturns, rather than moving into the interior of the circulation. A simple model that can account for the elemental and isotopic composition of ocean island basalts forms their sources by the addition of metasomatic melt to the undcplcUd MORB source while it forms the lower part of the mechanical boundary layer beneath continents. The isotopic differences between ocean island basalt and MORB are generated before the source becomes entrained in the cold sinking plumes that fall to the base of the convecting layer. At the base the material is heated and rises as part of a hot plume. Because the metasomatic melt contains water and carbonates, the enriched regions start to melt and generate more melt on decompression than does the MORB source. Such regions can therefore generate islands and seamounts. Even when the enriched material moves into the interior of the circulation and acquires the mean potential temperature of the mantle, it will still generate more melt on decompression than will the MORB source, and the isotopic and elemental composition will still be distinctive. The model can therefore account for the observed composition of magmas from seamounts that cannot be produced from either the MORB or the primitive source.

Nonlinear Equilibration of Two-Dimensional Eady Waves: Simulations with Viscous Geostrophic Momentum Equations

Abstract Equilibration of two-dimensional Eady waves is numerically investigated using the geostrophic momentum equations incorporating heat and momentum diffusion. Extended solutions are obtained beyond what would be the collapse of surface fronts in the inviscid theory, and are found to accurately reproduce the equilibration of baroclinic waves simulated with the primitive equations. Potential vorticity anomalies produced at the surface fronts are essential in the initial amplitude saturation and in the asymptotic behavior of the equilibrated flow. A supergeostrophic shear spun up nonlinearly in the zonal flow also plays an important role in causing the reversal of the tilt. The zonal mean potential temperature profile in the equilibrium state is similar to the prediction by the adjustment hypothesis of Gutowski when only horizontal diffusion is present. However, it is closer to an Eady's basic state with enhanced static stability when vertical diffusion is also present. The difference in the ageostroph...

Mixed-layer heat advection and entrainment during the sea breeze

A model is developed to simulate the potential temperature and the height of the mixed layer under advection conditions. It includes analytic expressions for the effects of mixed-layer conditions upwind of the interface between two different surfaces on the development of the mixed layer downwind from the interface. Model performance is evaluated against tethersonde data obtained on two summer days during sea breeze flow in Vancouver, Canada. It is found that the mixed-layer height and temperature over the ocean has a small but noticeable effect on the development of the mixed layer observed 10 km inland from the coast. For these two clear days, the subsidence velocity at the inversion base capping the mixed layer is estimated to be about 30 mm s−1 from late morning to late afternoon. When the effects of subsidence are included in the model, the mixed-layer height is considerably underpredicted, while the prediction for the mean potential temperature in the mixed layer is considerably improved. Good predictions for both height and temperature can be obtained when values for the heat entrainment ratio,c, 0.44 and 0.68 for these two days respectively for the period from 1000 to 1300 LAT, were used. These values are estimated using an equation including the additional effects on heat entrainment due to the mechanical mixing caused by wind shear at the top of the mixed layer and surface friction. The contribution of wind shear to entrainment was equal to, or greater than, that from buoyant convection resulting from the surface heat flux. Strong wind shear occurred near the top of the mixed layer between the lower level inland flow and the return flow aloft in the sea breeze circulation.

Quasi‐stationary planetary waves in total ozone and their correlation with lower stratospheric temperature

Hemispheric maps of monthly mean total ozone display distinct waves of low zonal wavenumbers during winter months. In addition, there is a strong and statistically significant spatial correlation between the total ozone perturbation and the temperature perturbation in the lower stratosphere. Previous attempts at an explanation of the correlation appear somewhat unsatisfactory. In the current paper the climatological behavior for southern hemisphere October is investigated. Specifying the dynamics from observations in the linearized stationary ozone continuity equation, one can simulate the lowest wavenumbers of the hemispheric total ozone perturbation. Both vertical and horizontal advection substantially contribute to the total ozone perturbation, with significantly different patterns each. A conceptual picture for the correlation is developed, which accounts for both advection contributions. The slopes of lower stratospheric zonal mean potential temperature and ozone mixing ratio turn out to be important. Furthermore, the feasibility of a Matsuno‐type model for the waves in total ozone is shown.

The mean ozone profile and its temperature sensitivity in the upper stratosphere and lower mesosphere: An analysis of LIMS observations

A detailed analysis of one week (May 1–7, 1979) of data from the Nimbus 7 Limb Infrared Monitor of the Stratosphere (LIMS) is presented, with emphasis on the ozone abundance and its temperature sensitivity between 0.1 and 6 mbar, covering the upper stratosphere and lower mesosphere. The time period was chosen to minimize possible ozone transport from large‐scale dynamical disturbances. The zonally averaged ozone profile (30°–35°N latitude) is compared with results from a simplified photochemical model that assumes ozone to be in photochemical steady state. The model is constrained by the simultaneous LIMS observations of temperature, H2O, and NO2. Such constraints for both the stratosphere and mesosphere have not been available prior to the LIMS data set. The model ozone profile is systematically lower than the observed profile, which is in good agreement with the observations of other experiments below ∼0.2 mbar. However, the calculated uncertainties in the model values do overlap the range defined by the observational uncertainties. Certain key parameters are identified, changes in which can systematically increase the ozone profile in both the stratosphere and mesosphere. In particular, changes in O2 photolysis and O3 formation could eliminate most of the differences in the whole altitude range. Thus one does not have to invoke one or more missing key reactions in current photochemical models in order to explain this systematic discrepancy. The LIMS‐derived values for the sensitivity of ozone to changes in temperature, ΘL, are compared with equilibrium model calculations, ΘE, which include the temperature‐driven opacity feedback effect on photodissociation rate constants. Given the noise of the data, there is fair agreement in the mesosphere, but below 1 mbar, ΘL/ΘE decreases with increasing pressure. Uncertainties in the photochemical model (or in the data) cannot account for this discrepancy. The theoretical ozone response to temperature perturbations is investigated. We show how, in general, the ozone‐temperature sensitivity coefficient, Θ, is affected by zonal and vertical advection terms as well as by the photochemical coupling between O3 and T. Zonal advection produces a Doppler shift of the wave frequency, thereby affecting the ozone‐temperature sensitivity at a fixed point. Vertical wave advection can be strong enough (for local gravity waves) to lead to an “advective equilibrium” situation, whereby ozone and temperature changes (reflected in Θ) merely follow the vertical gradients of mean ozone and potential temperature. Long (greater than a week) period planetary‐scale waves, on the other hand, do not act fast enough to perturb ozone away from photochemical equilibrium (at least above about 5 mbar). The theoretical Θ values for the lower mesosphere are close to the photochemical values, for waves other than short (less than a day) period gravity waves. In the upper stratosphere the LIMS‐derived Θ values can be explained by a combination/superposition of waves with 1‐ to 5‐day periods. Simultaneous observations of ozone and temperature in the middle atmosphere can provide indirect information about wave activity (frequency). The parameter ΘE is not very sensitive to changes in model photochemistry. Similarly, “observed Θ” is not a very good indicator of potential future changes in the photochemistry caused by chlorine increases.

A moving grid finite-element model of the bulk properties of the atmospheric boundary layer

A moving-grid finite-element model has been developed to model numerically the vertically integrated properties of the atmospheric boundary layer (ABL) in one dimension. The model equations for mean wind velocity and potential temperature are combined with a surface energy budget and predictive equations for boundary-layer height to simulate both stable and unstable ABLs. The nodal position defining the top of the boundary layer is one of the model unknowns and is determined by boundary-layer dynamics. The finite-element method, being an integral method, has advantages of accurate representation of both bulk values and their vertical derivatives, the latter being essential properties of the nocturnal boundary layer. Compared with observations and results of other models, the present model predicts bulk properties very well while retaining a simple and economical form.

On the mean monthly equivalent potential temperature and rainfall in West Africa

Rainfall in West Africa is examined in relation to monthly mean equivalent potential temperature (θe)at the earth's surface. The study revealed that monthly mean equivalent potential temperature (θe) and monthly rainfall (R) generally decreased northwards from the equator.

The Sea-Breeze Front Analytical Model

Abstract Analytical solutions to the nonlinear equations of motion are used to describe the sea breeze front. It is found that the front can develop when the atmosphere stratification in the heated layer is neutral or unstable. The temperature drop due to front passage is proportional to the square of the difference between the front speed and the synoptic wind. This square of the difference, on the other hand, is proportional to [2θ(s)/θm]ga where θ(s) is the mean potential temperature drop across the front and a is the front radius. Fronts which have the same speed of propagation and size, have a larger temperature drop when the synoptic wind blows in the opposite direction to the direction of propagation. Onshore winds associated with strong convergence are obtained in the lower part of the front, while the return current associated with strong divergence is observed in the upper part. The vertical velocity reaches values of some meters per second in the front region. The front propagation is studied...

Evidence and Interpretation of a Spectral Gap in the Turbulent Atmospheric Temperature Spectra

An analytical formulation of the turbulent potential energy spectrum in a stably stratified medium, valid in the inertia buoyancy subrange, is deduced in the framework of classical assumptions (no source, no sink, spectra locality and proportionality of the buoyancy flux to the mean potential temperature gradient) using recently published results of J. Weinstock. This formulation predicts a gap between two spectral ranges where temperature fluctuations mainly result from either turbulent advection or vertical displacements of fluid particles. In the former, the spectrum reduces to the well-known Obbukov-Corrsin-5/3 power law while in the latter, it becomes proportional to the kinetic energy spectrum, with a −3 spectral slope and a reverse potential energy flux. Experimental evidence obtained in the stratosphere supports this theoretical description.

The Relationship between Tropopause Potential Temperature and the Buoyant Energy of Storm Air

It has been suggested that the potential temperature of the tropical tropopause may be linked to the energy of air flowing into storms, and Previous studies have sought to correlate the subannual fluctuations of the two quantities. The formulations used in these studies also provide estimates of the mean tropopause potential temperatures, but such temperatures are much lower than the observed values. In this work we reexamine the problem. The earlier thermodynamic formulation is replaced by a more accurate form, and the appropriate humidity content of storm air is introduced and justified. The data now show that, averaged over the tropical ocean regions, the mean potential temperature of the tropopause is determined accurately and directly by the mean sea surface temperature. Continental conditions are significantly different and require further study. It appears desirable to undertake detailed investigations of the local relationship between surface storm conditions and tropopause characteristics.

Characteristics of thermohaline steps off the northeast coast of South America, July 1983

XBT and CTD measurements made in the Atlantic Ocean southeast of Barbados reveal a series of large thermohaline steps lying between the salinity maximum of the Subtropical Underwater at about 100 m and the salinity minimum of the Antarctic Intermediate Water at about 800 m. Historical data indicate that the steps are a permanent feature of the area extending over some 10 6 km 2. At two multicast stations in July 1983 the average step was 19.0 dbar in thickness, and the average interface between steps was 2.1 dbar thick. Mean potential temperature, salinity and potential density changes across the interfaces were, respectively, 0.526°C, 0.084 psu, and 0.030. Internal structure was noted in some of the steps, as well as features resembling intrusions. The low value of the density ratio, approximately 1.5, supports the hypothesis that the steps are caused by intense salt finger activity. Estimates of vertical fluxes of heat and salt through the staircases are large enough to suggest that the process plays a major role in vertical exchange across the thermocline in this region and, consequently, a major role in determining the T-S properties of the equatorial thermocline and of the Caribbean Current-Gulf Stream system.

14C in the Deep Water of the East Atlantic

The renewal of east Atlantic deep water and its large-scale circulation and mixing have been studied in observed distributions of temperature, silicate, ΣCO2, and 14C. 14C variations in northeast Atlantic deep water below 3500m depth are small. Δ14C values range from − 100‰ to −125‰. 14C bottom water concentrations decrease from Δ14C =−117‰ in the Sierra Leone Basin to Δ14C = − 123‰ in the Iberian Basin and are consistent with a mean northward bottom water flow. The characteristic of the water that flows from the west Atlantic through the Romanche Trench into the east Atlantic was determined by inspection of θ/Δ14C and θ/SiO2 diagrams. A mean potential temperature of θ = 1.50 ± .05°C was found for the inflowing water. A multi-box model including circulation, mixing, and chemical source terms in the deep water has been formulated. Linear programing and least-squares techniques have been used to obtain the transport and source parameters of the model from the observed tracer fields. Model calculations reveal an inflow through the Romanche Trench from the west Atlantic, which predominates over any other inflow, of (5 ± 2) Sv (potential temperature 1.50°C), a convective turnover of (150 ± 50) years and a vertical apparent diffusivity of (4 ± 1) cm2/s. Chemical source terms are in the expected ranges.

The disappearance of the long term meromictic stratification of the Dead Sea

Following a lowering of its surface level by 3.5–4 m, the water of the Dead Sea turned over in February 1979, ending a long period of stratification. The “classic” structure (a salinity gradient at a depth of 30–40 m separating the surface layers, through a transitional zone, from a “fossil” water spreading from 60 to 80 m to the bottom 320 m) was replaced by a reduction of the salinity difference between surface and deep waters from 25 g kg−1 in 1960 (50 g kg−1 in 1864) to 3 g kg−1 in 1975, and to <0.1 g kg−1 in 1978, and by a series of deepenings of the interface between the fossil waters and the upper, seasonally variable layers, from about 80‐m depth in 1975 to 180 m in 1978. The “eroded” deep waters maintained their original properties (mean salinity 275.8 g kg−1, mean potential temperature 21.34°C, mean density 1.2334 g cm−3, and tritium content 0.1 TU). In February 1979 the entire water column was essentially homogeneous and stable (Brunt‐Väisälä frequency 5.8 × 10−4 s−1), with temperature, salinity, and density somewhat higher than those of the former deep waters.The successive deepenings and the complete overturn were caused when the surface (10–25 m) layers cooled during autumn and winter from 37° to 18°C, and, following each dry year, reduced their excess salinity (3 g kg−1) by vertical mixing to a greater depth than in the previous winter. The meromixis of the Dead Sea is ectogenic, caused by freshwater inflow over hypersaline deep layers. The imbalance between the effects of salinity and temperature changes on the density of the water column, and variations (both natural and artificial) in amount and timing of the inflow rate, cause the seasonal changes of the water column to be nonrepetitive; the cumulative extreme development of this is an overturn.

Entrainment effects in the well-mixed atmospheric boundary layer

We discuss the structure and evolution of a cloud-free atmospheric boundary layer (ABL) during daytime over land, starting from a shallow ABL at sunrise and developing into a deep ABL with strong convection in the afternoon. The structure of the turbulence in the lower half of a convective ABL capped by an inversion is reasonably well understood. Less is known about the details of the turbulence in higher regions affected by entrainment, because of the difficulty in taking turbulence measurements there. For the evolution in time of the height of the ABL and its mean potential temperature mixed-layer models have been developed that give satisfactory agreement with observations. It has been shown that for many practical applications accurate knowledge of forcing functions and boundary conditions is more important than a refinement of the entrainment hypothesis. Observations show that the assumption of well-mixedness of first-order moments of conservative variables is not valid for all quantities. A simple similarity relation for the inclusion of the effect of entrainment on the shape of the vertical profiles is given.

Models and observations of the growth of the atmospheric boundary layer

The evolution of the mixed layer during a clear day can be described with a slab model. The model equations have to be closed by a parameterization of the turbulent kinetic energy budget. Several possibilities for this parameterization have been proposed. In order to assess the practical applicability of these models for the atmosphere, field experiments were carried out on ten clear days in 1977 and 1978. Within the accuracy of the measurements the mixed-layer height in fully convective conditions (at noon on clear days) is well predicted taking a constant heat flux ratio % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0Yaa0% aaaeaacqaH4oqCcaWG3bWaaSbaaSqaaiaadIgaaeqaaaaakiabg2da% 9iaaicdacaGGUaGaaGOmamaanaaabaGaeqiUdeNaam4DamaaBaaale% aacaWGZbaabeaaaaaaaa!41D4!\[ - \overline {\theta w_h } = 0.2\overline {\theta w_s } \]. In the early morning hours mechanical entrainment is also important. Good overall results are obtained with the entrainment formulation % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0Yaa0% aaaeaacqaH4oqCcaWG3bWaaSbaaSqaaiaadIgaaeqaaaaakiabg2da% 9iaaicdacaGGUaGaaGOmamaanaaabaGaeqiUdeNaam4DamaaBaaale% aacaWGZbaabeaaaaGccqGHRaWkcaaI1aGaamyDamaaDaaaleaacqGH% xiIkaeaacaaIZaaaaOGaamivaiaac+cacaWGNbGaamiAaaaa!49C1!\[ - \overline {\theta w_h } = 0.2\overline {\theta w_s } + 5u_ * ^3 T/gh\]. Only large differences in the entrainment coefficients lead to significantly different results. Making the entrainment model more complex does not lead to substantial improvement. The mean potential temperature in the mixed layer is reproduced within 0.5 °C. This temperature is insensitive to the choice of a particular entrainment formulation and depends more on the surface heat input and the temperature gradient in the stable air aloft.

中立接地気層における乱流統計諸量の解析解

A turbulence model is proposed for the prediction of the asymptotic behavior of turbulence statistics in neutral surface layer. Following equations are analytically investi-gated: ones for the second-order moments of turbulence, and one for its length scale. A few empirical assumptions are made for the turbulent transport terms in the equations of second-order moments. With the present model, are deductively obtained the well-known semiempirical results: the turbulent length scale proportional to the mixing length, and the logarithmic vertical distributions for the mean wind velocity and the mean potential temperature. The asymptotic solutions of kinematic and thermal second-order moments of turbulence are also obtained.

The bottom mixed layer on the continental shelf

The height of the bottom mixed layer of the continental shelf is defined as the height above bottom where the mean potential temperature exceeds the bottom value by 0.01 °C. Direct measurements of vertical current shear and temperature structure indicate that in this region the production of turbulent energy is much greater than the stabilizing effect of the heat flux down the potential temperature gradient. Detailed temperature profiles with a resolution of 10 −3 °C suggest that the controlling parameters for the potential temperature gradient are the friction velocity and the downward heat flux.