Heat Flux in the Coastal Zone

Various difficulties with application of Monin–Obukhov similarity theory are surveyed including the influence of growing waves, advection and internal boundary-layer development. These complications are normally important with offshore flow. The transfer coefficient for heat is computed from eddy correlation data taken at a mast two kilometres off the Danish coast in RASEX. For these coastal zone data, the thermal roughness length shows no well-defined relation to the momentum roughness length or roughness Reynolds number, in contrast to previous theories. The variation of the momentum roughness length is dominated by wave state. In contrast, the thermal roughness length shows significant dependence on wave state only for small values of wave age where the mixing is apparently enhanced by wave breaking. The development of thin internal boundary layers with offshore flow substantially reduces the heat transfer and thermal roughness length but has no obvious influence on momentum roughness length. A new formulation of the thermal roughness length based on the internal boundary-layer depth is calibrated to the RASEX data. For the very stable case, the turbulence is mainly detached from the surface and existing formulations do not apply.As an alternative to adjusting the thermal roughness length, the transfer coefficient is related directly to the stability and the internal boundary-layer depth. This avoids specification of roughness lengths resulting from the usual integration of the non-dimensional temperature function. The resulting stability function is simpler than previous ones and satisfies free convection similarity theory without introduction of the gustiness factor. The internal boundary layer also influences the moisture transfer coefficient.     

Variational principle of instability of atmospheric motions

Problems of instability of rotating atmospheric motions are investigated by using nonlinear governing equations and the variational principle. The method suggested in this paper is universal for obtaining criteria of instability in all models with all possible basic flows. For example, the model can be barotropic or baroclinic, layer or continuous, quasi-geostrophic or primitive equations; the basic flow can be zonal or nonzonal, steady or unsteady.Although the basic flows possess a great deal of variety, they all are the stationary points in the functional space determined by an appropriate invariant functional. The basic flow is an unsteady one if the conservation of angular momentum is included in the associated functional.The second variation, linear or nonlinear, gives the criteria of instability. Especially, the general criteria of instability for unsteady basic flow, orographically disturbed flow as well as nongeostrophic flow are first obtained by the method described in this paper.It is also shown that the difference between the criteria of instability obtained by the linear theory and our variational principle clearly indicates the importance of using nonlinear governing equations.In the appendix the theory is extended to cases such as in a β-plane where the fluid does not possess finite total energy, hence the variational principle can not be directly applied. However, a generalized Liapounoff norm can still be obtained on the basis of variational consideration.     

Spatial differences in seasonal variation of the upper-tropospheric jet stream in the Northern Hemisphere and its thermal dynamic mechanism

NCEP/NCAR reanalysis daily data from 1951 to 2008 are used in this study to reveal the spatial-asymmetric features in the seasonal variation of the upper-tropospheric jet stream (UTJS) and its thermal dynamic forcing mechanism. The jet occurrence percentage distribution of the UTJS demonstrates a spiral-like pattern in winter, but it is quasi-annular in summer. The jet occurrence percentage in the Eastern Hemisphere is larger than that in the Western Hemisphere, and its maximum area is located further south. The polar front jet stream (PJS) and subtropical jet stream (SJS) can be distinguished over the Northern Africa and Asian regions, whereas only one jet stream can be observed over the Western Pacific and Atlantic Ocean. Furthermore, a single peak pattern is found in the seasonal variation of the SJS occurrence frequency with the highest jet occurrence appearing in winter and the lowest in summer, while a double peak pattern is observed in the seasonal variation of the PJS occurrence, i.e., the jet occurrence reaches its peaks in autumn and spring for the PJS. Based on the thermal wind theory, air temperature gradient and atmospheric baroclinicity are calculated and compared with the jet occurrence variation to explore the thermal dynamic forcing mechanism for the UTJS variation. In addition, synoptic-scale transports of eddy heat and momentum are also calculated. The results indicate that the SJS variation is primarily determined by the air temperature gradient and atmospheric baroclinicity, while the PJS variation is under great influence of the transport of eddy heat and momentum over Northern Africa and East Asia. The UTJS variation over the area from 140E to 70W cannot be well individually explained by the air temperature gradient and atmospheric baroclinicity. Further analysis indicates that UTJS variation over this area is largely under control of combined effect of the transport of eddy heat and momentum as well as the atmospheric baroclinicity.     

An efficient PBL model for global circulation models-design and validation

An efficient, pianetary boundary layer (PBL) model is developed and validated with empirical data for applications in general circulation models (GCMs). The purpose of this PBL model is to establish the turbulent surface fluxes as a function of the principal external PBL parameters in a numerically efficient way. It consists of a surface layer and a mixed layer matched together with the conditions of constant momentum and heat flux at the interface. An algebraic solution to the mean momentum equations describes the mixed-layer velocity profile and thus determines the surface wind vector. The velocity profile is globally valid by incorporating the effect of variable Coriolis force without becoming singular at the equator. Turbulent diffusion depends on atmospheric stability and is modeled in the surface layer by a drag law and with first-order closure in the mixed layer. Radiative cooling in the stably stratified PBL is considered in a simple manner. The coupled system is solved by an iterative method. In order to preserve the computational efficiency of the large-scale model, the PBL model is implemented into the GISS GCM by means of look-up tables with the bulk PBL Richardson number, PBL depth, neutral drag coefficient, and latitude as independent variables.A validation of the PBL model with observed data in the form of Rossby number similarity theory shows that the internal feedback mechanisms are represented correctly. The model, however, underpredicted the sensible heat-flux. A subsequent correction in the turbulence parameterization yields better agreement with the empirical data. The behavior of the principal internal PBL quantities is presented for a range of thermal stabilities and latitudes.     

Bulk Formulation of the Surface Heat Flux

An interpretive literature survey examines different approachesfor applying the bulk aerodynamic formulato predict the surface heat flux. The surface heat flux is often predicted in terms of the surface radiation temperature, which is also used to predict the upward longwave radiation and the heat flux into the soil. In models, the thermal roughness length based on the surface radiation temperature (radiometric roughness length) is often specified to be smaller than the roughness length for momentum for a number of distinct reasons. The definition of the radiometric roughness length depends on the way that the surface temperature is measured, the choice of stability functions and displacement height and inclusion of any additional resistances.Using airborne eddy correlation data collected over eight different sites including bare soil, crops and grassland and several types of forests, the radiometric roughness length is found to vary by orders of magnitude in a manner that is difficult to formulate. Alternatively, we evaluate the approach where the thermal roughness length is equated with the better behaved roughness length for momentum and the corresponding aerodynamic surface temperature is modelled in terms of the surface radiation temperature, solar radiation, and vegetation index. The influence of wind speed and soil moisture on the difference between the aerodynamic and surface radiation temperatures is also examined.     

Parameterization of a momentum source in a tropical cumulus ensemble

Summary An eddy effect of tropical deep convection on the large-scale momentum, resp vorticity budget is investigated. The process is specified by a simple parameterization approach which is based on a concept of rotating clouds exerting a momentum on the large-scale flow. The cloud rotation is associated with the thermal properties of a cloud ensemble by the principle of conservation of potential vorticity. A decomposition of cloud classes is applied in consistency with the thermodynamical parameterization scheme of Arakawa and Schubert (1974).The parameterization is tested with observations of GATE74, Phase III. The data are processed on a B/C-scale grid (55km) in a region within 9N and 16N, and between 21W and 27W, and with a vertical resolution of 41 levels. The parameterization results correspond to the observed patterns, especially in situations with strong large-scale wind shear. The findings suggest that certain large-scalle flow regimes provoke convective scale momentum generation rather than redistributing large-scale momentum by convective circulations.With 10 Figures     

The dynamic mechanism of the formation of the low level jet

The ordinary multidimensional reductive perturbation method is generalized so as to apply to the general case including the dissipative factor. With this the corresponding Cubic-Schrödinger equation is deduced, and by the preliminary study of its solution, it shows that it is more admissible to consider atmospheric meso-scale systems as the nonlinear Cubic-Schrödinger waves. With suitable boundary and initial conditions, the Cubic-Schrödinger equation is numerically integrated so as to investigate the possible dynamic mechanism as well as the impacts of the nonlinear action, turbulent friction and topogrphy to the formation of the LLJ. The results indicate that the downward transfer of the momentum and the effect of the surface friction are responsible for the concentration of the momentum in the layer between 850 and 700 hPa. The location of the horizontal concentration of momentum depends on the propagation of momentum, in the process the inertia-gravity internal wave is very important, whereas turbulent friction is unfavourable for or delays the formation of the low level jet.     

On the Angular Momentum Loss of Tropical Cyclones: An <Emphasis Type="Italic">f</Emphasis>-Plane Approximation

The angular momentum for ideal axisymmetric tropical cyclones on the f-plane is investigated with a focus on the total-volume integrated quantity. Budget analysis of the momentum equation at cylindrical coordinates shows that a tropical cyclone loses angular momentum during its development and mature stages due to the dynamical difference between the viscous inward-flow near the surface and the angular momentum conserving outward-flow aloft. The total relative angular momentum of a tropical cyclone, as a result, can be negative (i.e., implying anticyclonic rotation as a whole) despite intense cyclonic wind in the tropospheric layers. This anticyclonic rotation was measured in terms of the super-rotation ratio, the ratio of total relative angular momentum to the planetary angular momentum. Simulations with the numerical model of Weather Research and Forecasting (WRF) version 3.4.1 was found to be in favor of the theoretical angular-momentum budget analysis. It was revealed in the numerical simulations that the super-rotation ratio was negative, indicating a sub-rotation, as was predicted by analysis. The sub-rotation ratio was found to be less than one percent for typical tropical cyclones. To show the angular momentum decrease even in the decaying stage, numerical simulations where the thermal forcing by sea surface temperature switched off in the mature stage were carried out. In support of the angular momentum budget analysis, the results indicated that the angular momentum also decreases for a while soon after the forcing was eliminated.     

Theoretical determination of the surface energy balance and thermal regimes of bare soils

An analytical theory that determines the thermal regimes in the soil and the thermal and moisture regimes in the atmosphere for bare surfaces is derived. Both soil and atmospheric thermal properties are assumed to be power functions of depth and height, respectively. Evaporation is determined using a surface resistance to vapour flow. Fourier superposition is used to represent nonsinusoidal variations in time due to effects such as variable cloud cover. The theory is in acceptable agreement with micrometeorological measurements made at two bare soil sites of contrasting surface bulk density. It is concluded that the surface resistance model for evaporation is applicable to bare soils which remain wet at depth, particularly if their surface is loosened. The theory is used to predict the diurnal thermal regimes of saturated and dry sand, loam, and peat soils.     

A first-order closure scheme to describe counter-gradient momentum transport in plant canopies

The gradient diffusion parameterization of the Reynolds stress is modified by adding a bulk momentum transport term. Comparisons to available data indicate that this term accounts for the gusts or downsweeps of higher momentum fluid into the canopy and ejections of lower momentum fluid out of the canopy. This term results in realistic mean wind speed profiles.     

Mathematical Derivation of Spatially-Averaged Momentum Equations for an Urban Canopy Model Using Underlying Concepts of the Immersed Boundary Method

We propose a new approach to derive spatially-averaged momentum equations for an urban canopy model that resolves buildings vertically and not horizontally. First, in order to mathematically describe the actual momentum field as a completely continuous field, the underling concepts of the immersed boundary method are employed, where we assume that (i) the entire simulation space, including that occupied by buildings, is filled with a fluid, and (ii) an external body force field exists that reduces the wind speed to zero at all positions coinciding with the space occupied by the buildings. Then, in order to obtain the required spatially-averaged momentum equations in a self-consistent manner, a spatial-averaging operation is applied to the Navier–Stokes equations that include a term representing the external force field. The applied spatial-averaging operation is equivalent to the conventional spatial filtering operation used in large-eddy simulations. To examine the significance of the subgrid-scale (SGS) stresses of the spatially-averaged momentum equations, a numerical simulation is performed for a flow around a regular array of cubical blocks with a grid resolution that is sufficient to resolve the blocks. By estimating the individual terms in the spatially-averaged momentum equations using the simulation results, we show that the SGS stresses contribute significantly to the spatially-averaged momentum budget, and therefore they should not be neglected in urban canopy modelling.     

大气热力强迫和动力强迫的调配及平均经圈环流的仿真模拟

通过研究平均经围环流（ＭＭＣ）及其所受的内外强迫作用的相互配置，指出对ＭＭＣ的热力和动力强迫满足确定的调配率。这一调配率受大气内在的斜压性、静力稳定度及绝对涡度制约。利用辐射加热和凝结加热参数化方案，结合欧洲中期天气预报中心（ＥＣＭＷＦ）的分析资料，对１月份平均经围环流进行数值仿真模拟。结果表明，热带对流加热可以形成双层Ｈａｄｌｅｙ环流结构；涡动动量输送对双Ｈａｄｌｅｙ环流的形成也有一定影响。中高纬度的ＭＭＣ则主要由外动量强迫及大气的动量和热量输送特征决定。     

MODULATION OF ATMOSPHERIC THERMAL AND MECHANICAL FORCINGS AND NUMERICAL MODELING OF MEAN MERIDIONAL CIRCULATION

Upon investigating the relative locations of internal and external forcing and the resultant mean meridional circulation,it was found that thermal forcing and mechanical forcing for the formation of atmospheric mean meridional circulation are modulated by a certain ratio.This ratio is determined by the inherent baroclinity,static stability and absolute vorticity of the atmosphere.By employing a parameterization scheme for radiative heating and condensation heating,together with the analysisdata of the European Center for Medium-range Weather Forecasts,the mean meridional circulation for January wassimulated numerically.It was found that latent heat release in the tropics may result in the formation of double-layeredHadley circulation,so do the eddy momentum transfer processes.On the other hand,mean meridional circulations in extra-tropics are mainly determined by external momentum forcing and atmospheric properties of eddy momentum andheat transfer.     

Regional Fluxes Of Momentum And Sensible Heat Over A Sub-Arctic Landscape During Late Winter

Based on measurements at Sodankylä Meteorological Observatory the regional (aggregated) momentum and sensible heat fluxes are estimated for two days over a site in Finnish Lapland during late winter. The forest covers 49% of the area. The study shows that the forest dominates and controls the regional fluxes of momentum and sensible heat in different ways. The regional momentum flux is found to be 10–20% smaller than the measured momentum flux over the forest, and the regional sensible heat flux is estimated to be 30–50% of the values measured over a coniferous forest.The regional momentum flux is determined in two ways, both based on blending height theory. One is a parameterised method, the other represents a numerical solution of an aggregation model. The regional sensible heat flux is determined from the theory of mixed-layer growth. At near neutral conditions the regional momentum flux can be determined independently of the regional sensible heat flux. At unstable conditions the two models become coupled.The information that is needed by the parameterised blending height method and by the mixed-layer evolution method in order to derive the regional fluxes of momentum and sensible heat can be obtained from radiosonde profiles of wind speed and temperature.     

The Distribution and Uncertainty Quantification of Wind Profile in the Stochastic General Ekman Momentum Approximation Model

The general Ekman momentum approximation boundary-layer model(GEM) can be effectively used to describe the physical processes of the boundary layer. However, eddy viscosity, which is an approximated value, can lead to uncertainty in the solutions. In this paper, stochastic eddy viscosity is taken into consideration in the GEM, and generalized polynomial chaos is used to quantify the uncertainty. The goal of uncertainty quantification is to investigate the effects of uncertainty in the eddy viscosity on the model and to subsequently provide reliable distribution of simulation results. The performances of the stochastic eddy viscosity and generalized polynomial chaos method are validated based on three different types of eddy viscosities, and the results are compared based on the Monte Carlo method. The results indicate that the generalized polynomial chaos method can be accurately and efficiently used in uncertainty quantification for the GEM with stochastic eddy viscosity.     

Oscillations in a simple air-water system driven by a stabilizing heat flux

An air-water system coupled by heat and stress is modelled by two interacting fluid loops. When heated from above and cooled from below the system can become unstable and self-sustained oscillations develop, whereas a single fluid system is stable in the same situation. The oscillations are explained by thermal lag between the loops. The water loop oscillates stably under its restoring buoyancy torque but the coresponding air oscillations, generated by heat conduction from the water loop, lag by roughly half a period, and the air stress therefore acts to amplify rather than damp oscillations in the water loop.     

Turbulent transport within and above a maize canopy

Hot-wire anemometers were used to measure air temperature and the three velocity components of the wind within and above a maize canopy. From digitized anemometer outputs, correlation coefficients for vertical heat flux and turbulent momentum transfer were calculated. A comparison of these coefficients with profiles of mean wind speed and mean temperature indicates that the main features of the turbulence may be explained in terms of the usual mixing-length theory. Instantaneous records of heat and momentum flux, however, indicate the existence of other competing turbulent mechanisms due to the unsteady, non-equilibrium nature of the turbulent flow. Regimes of flow dominated by mechanical and/or thermal mixing are indicated. Spectral results show that high shear and turbulent intensity levels as well as the presence of the maize leaves and stalks as vortex-shedding surfaces complicate the energy transfer mechanism. An energy balance between radiation and convection reveals that the energy budget is primarily a balance between solar radiation and the flux of latent heat.Contribution of the Sibley School of Mechanical and Aerospace Engineering, Cornell University, in cooperation with the Agricultural Research Service, U.S. Department of Agriculture, Ithaca, N.Y., U.S.A. and the Cornell University Agricultural Experiment Station. Department of Agronomy Series No. 1116.Sibley School of Mechanical and Aerospace Engineering, Cornell University; U.S. Department of Agriculture, Gainesville, Florida Section for Estuary and Fjord Studies, River and Harbour Laboratory, Technical University of Norway, Trondheim, Norway; State Univ. of New York at Buffalo; and U.S. Department of Agriculture and Cornell University; respectively.     

Low-Frequency CISK-Rossby Wave and Stratospheric QBO in the Tropical Atmosphere

1.IntroductionThelow~frequencyoscillation(LFO)isaveryimPOrtantweatherphenomenonintheatmosphere.The30--50--dayandquasichiweeklyoscillationsinthetropicalatmospherearemostintensivelystudied,andcomParativelyspeaking,anotherkindofLFOconcernillgtheQBOofthestratosphericzonalwindsismuchlessstudied,which,althoughoccurringinthestratosphere,bearsacloserelationtothetroposphericactivitiesandtheevolutionoflow--latitudecirculationssothatitisworthwhiletoexploreindepththephysicalmechanismfortheQBOoccurre…     

Density intrusions with large relative thickness

Previous analyses of density intrusions indicate that only relatively thin intrusions are allowed, to satisfy a momentum balance at the current head. These constraints can be relaxed somewhat by various modifications to the basic theory, but are inconsistent with experimental observations indicating that intrusions occupying nearly the entire flow depth can be produced. An alternative theory of density current propagation does not possess these restrictions on intrusion layer thickness and provides a more satisfactory explanation of experimental observations. New experimental results are presented to corrborate this interpretation.