A generalized combination equation derived from a multi-layer micrometeorological model

The discrete multi-layer model originally devised by Waggoner and Reifsnyder (1968) is used as a theoretical basis to describe the vegetation-atmosphere interaction. Mathematical development of the basic equations yields Ohm's law-type formulae for sensible and latent heat fluxes from which it is possible to derive a combination equation very close in form to Penman-Monteith's equation. A bulk aerodynamic resistance and a bulk stomatal resistance can be defined and expressed in terms of the elementary resistances of the multi-layer model. This new combination equation offers an alternative to the attempts undertaken by Shuttleworth (1976) to unify multi-layer and single-layer approaches.     

A Simple Single-Layer Urban Canopy Model For Atmospheric Models: Comparison With Multi-Layer And Slab Models

We developed a simple, single-layer urban canopy model, and comparedit to both multi-layer and slab models. Our single-layer model has thefollowing features: (a) It is a column model of energy and momentumexchange between an urban surface and the atmosphere, (b) it includesthe influence of street canyons, which are parameterized to representthe urban geometry, (c) it includes shadowing from buildings andreflection of radiation, and (d) it estimates both the surfacetemperatures of, and heat fluxes from, three surface types: roof, wall,and road. In the simulation of the single-layer model, the roof washottest during the daytime, but coolest from midnight to early morning.This is consistent with output from the multi-layer model and fieldobservations at a residential area on a clear, summer day. The diurnalvariation of the energy budget from the single-layer model agrees wellwith that from the multi-layer model. Our single-layer model'sperformance is nearly that of a multi-layer model for studyingmesoscale heat islands. Nevertheless, it is simply parameterized,and thus easily included in larger-scale atmospheric models. The slabmodel has the largest nighttime cooling rate of the three models. Toovercome this, it needs more adjustments than for the canopy models.     

An investigation of the morning dissipation of the valley wind by means of a one-dimensional model

A simple numerical model is constructed to investigate the time-history of the dissipation of the valley wind system. The local wind system is considered as a thermally induced circulation. The Coriolis force, effect of slope of the valley floor and advection of heat and momentum are not considered in this study. The non-dimensional forms of the heat-diffusion and momentum equations along the direction of the valley axis are numerically integrated with a set of specified initial conditions, boundary conditions and assumed heat sources (and sinks). Three cases are presented in this report. The numerical solutions are in good agreement with the observed features of the dissipation of the valley wind provided that a relative heat source at ridge-line level and a relative heat sink at the ground are hypothesized.The major part of the research presented in this paper was done while the author was at the Department of Meteorology and Oceanography, New York University.     

Simulation of snow processes beneath a boreal scots pine canopy

A physically-based multi-layer snow model Snow-Atmosphere-Soil-Transfer scheme(SAST)and a land surface model Biosphere-Atmosphere Transfer Scheme(BATS)were employed to investigate how boreal forests influence snow accumulation and ablation under the canopy.Mass balance and energetics of snow beneath a Scots pine canopy in Finland at different stages of the 2003-2004 and 2004 2005 snow seasons are analyzed.For the fairly dense Scots pine forest,drop-off of the canopy-intercepted snow contributes,in some cases,twice as much to the underlying snowpack as the direct throughfall of snow.During early winter snow melting,downward turbulent sensible and condensation heat fluxes play a dominant role together with downward net longwave radiation.In the final stage of snow ablation in middle spring,downward net all- wave radiation dominates the snow melting.Although the downward sensible heat flux is comparable to the net solar radiation during this period,evaporative cooling of the melting snow surface makes the turbulent heat flux weaker than net radiation.Sensitivities of snow processes to leaf area index(LAI)indicate that a denser canopy speeds up early winter snowmelt,but also suppresses melting later in the snow season. Higher LAI increases the interception of snowfall,therefore reduces snow accumulation under the canopy during the snow season;this effect and the enhancement of downward longwave radiation by denser foliage outweighs the increased attenuation of solar radiation,resulting in earlier snow ablation under a denser canopy.The difference in sensitivities to LAI in two snow seasons implies that the impact of canopy density on the underlying snowpack is modulated by interannual variations of climate regimes.     

Average fluxes from heterogeneous vegetated regions

Using a surface-layer model, fluxes of heat and momentum have been calculated for flat regions with regularly spaced step changes in surface roughness and stomatal resistance. The distance between successive step changes is limited to 10 km in order to fill the gap between micro-meteorological measurements and meso-scale models. A single-layer big leaf model of the vegetation is compared with a multi-layer model to assess the performance of the former in the determination of surface fluxes in heterogeneous terrain.The sub-models of vegetation and atmosphere are mainly based on well-known theory. However, a modification of the mixing-length closure of atmospheric exchange is included to achieve a more realistic calculation of fluxes near step changes at the surface. Measurements, presented in the literature, are used to determine the mixing-length parameters and to validate the calculated fluxes downwind of a change in vegetation cover.The single-layer model, well validated for homogeneous surfaces, underestimates the effects of local advection upon the surface fluxes as this model neglects air flow across the edges of tall vegetation. Using the multi-layer model, local advection results in an increase of up to 50% in regional momentum flux and smaller changes in regional evaporation. Even widely spaced heterogeneities appear to influence regional fluxes.     

A Sensitivity Study of Arctic Ice-Ocean Heat Exchange to the Three-Equation Boundary Condition Parametrization in CICE6

In this study, we perform a stand-alone sensitivity study using the Los Alamos Sea ice model version 6 (CICE6) to investigate the model sensitivity to two Ice-Ocean (IO) boundary condition approaches. One is the two-equation approach that treats the freezing temperature as a function of the ocean mixed layer (ML) salinity, using two equations to parametrize the IO heat exchanges. Another approach uses the salinity of the IO interface to define the actual freezing temperature, so an equation describing the salt flux at the IO interface is added to the two-equation approach, forming the so-called three-equation approach. We focus on the impact of the three-equation boundary condition on the IO heat exchange and associated basal melt/growth of the sea ice in the Arctic Ocean. Compared with the two-equation simulation, our three-equation simulation shows a reduced oceanic turbulent heat flux, weakened basal melt, increased ice thickness, and reduced sea surface temperature (SST) in the Arctic. These impacts occur mainly at the ice edge regions and manifest themselves in summer. Furthermore, in August, we observed a downward turbulent heat flux from the ice to the ocean ML in two of our three-equation sensitivity runs with a constant heat transfer coefficient (0.006), which caused heat divergence and congelation at the ice bottom. Additionally, the influence of different combinations of heat/salt transfer coefficients and thermal conductivity in the three-equation approach on the model simulated results is assessed. The results presented in this study can provide insight into sea ice model sensitivity to the three-equation IO boundary condition for coupling the CICE6 to climate models.     

多层模式中臭氧加热率的计算及其对大气温度场的影响

本文介绍一个简单、经济的适用于各种多层大气环流模式中计算臭氧加热率的参数化方案,利用这一方案,可根据臭氧总量气候观测值及其垂直分布资料计算臭氧加热率,也可以在模式中加入臭氧方程,用预报的臭氧含量计算臭氧加热率.用此方案对单站气候资料试算,结果指出,随着高度的增加,臭氧吸收太阳辐射对大气太阳加热率的贡献逐渐接近、达到并在平流层50hPa附近明显超过其它物质如水汽的贡献.此方案用于九层大气环流模式时,对其辐射加热率的计算有较理想的改进,并使模拟的大气温度垂直分布更符合观测事实.     

Test of a simple two-layer parameterisation to simulate the energy balance and temperature of a snow pack

Summary  Reasonably simple yet realistic modelling schemes simulating the heat and mass balance within a snow pack are required to provide the necessary boundary conditions for meteorological and hydrological models. An improvement to a one-layer snow energy balance model (UEB, Tarboton etal., 1995) is proposed to better simulate snow surface and snow pack temperatures and, as a result, snowmelt. The modified scheme is assessed against measured snow data from the WINTEX field campaign during spring 1997 in northern Finland, and compared with results from a complex multi-layer snow energy balance scheme. The results show that separation of a one-layer representation into two snow layers and a soil layer enables a more realistic simulation of soil and snow temperatures as well as of the snow surface temperature. The two-layer and the multi-layer snow schemes yielded comparable results for internal processes in the snow whenever the simulation was carried out under similar boundary forcing. The modified scheme is proposed for use as a sub-scheme in meteorological or hydrological models, or as a tool for simulating spatially-variable snowmelt and the surface energy balance during seasonal snow cover. Received November 18, 1999 Revised June 17, 2000     

一个长期降水预报的热力学模式

本文首先从大气水分平衡方程和地气系统热平衡方程出发,导出了描写降水和地温、气温相互联系的方程,然后根据土壤热传导方程,得到地温的预报方程,由此建立了一个长期降水预报模式。另外还对方程中与气候平均状态有关的参数的量级,根据实际资料进行了估算,对模式进行了合理的简化,为长期降水数值预报提出了一个实际可行的途径。     

Parameterization of Entrainment in a Sheared Convective Boundary Layer Using a First-order Jump Model

Basic entrainment equations applicable to the sheared convective boundary layer (CBL) are derived by assuming an inversion layer with a finite depth, i.e., the first-order jump model. Large-eddy simulation data are used to determine the constants involved in the parameterizations of the entrainment equations. Based on the integrated turbulent kinetic energy budget from surface to the top of the CBL, the resulting entrainment heat flux normalized by surface heat flux is a function of the inversion layer depth, the velocity jumps across the inversion layer, the friction velocity, and the convection velocity. The developed first-order jump model is tested against large-eddy simulation data of two independent cases with different inversion strengths. In both cases, the model reproduces quite reasonably the evolution of the CBL height, virtual potential temperature, and velocity components in the mixed layer and in the inversion layer.The part of this work was done when the first author visited at NCAR.     

An embedded mixed-layer-ocean circulation model

The rationale and numerical technique of embedding an oceanic bulk mixed-layer model with a multi-level primitive equation model is presented. In addition to the usual prognostic variables that exist in a multi-level primitive equation model, the embedded model predicts the depth of the well-mixed layer as well as the jumps in temperature and velocity that occur at the base of that layer. The depth of the mixed layer need not coincide with any of the fixed-model levels used in the primitive equations calculations.In addition to advective changes, the mixed layer can deepen by entrainment and it can reform at a shallower depth in the absence of entrainment. When the mixed layer reforms at a shallower depth, the vertical profile of temperature below the new, shallower mixed layer is adjusted to fit the fixed-level structure used in the primitive equations calculations using a method which conserves heat, momentum and potential energy. Finally, a dynamic stability condition, which includes a consideration of both the vertical current shear and the vertical temperature gradient, is introduced in place of the traditional ‘convective adjustment’.A two-dimensional version of the model is used to test the embedded model formulations and to study the response of the ocean to a stationary axisymmetric hurricane. The model results indicate a strong interdependence between vertical turbulent mixing and advection of heat.     

Analysis of Vertical Turbulent Heat Flux Limit in Stable Conditions with a Local Equilibrium, Turbulence Closure Model

Assuming that the vertical turbulent heat flux vanishes at extremely stable conditions, one should expect its maximal absolute value to occur somewhere at moderate stability, between a neutral and extremely stable equilibrium. Consequently, in some situations duality of solutions may be encountered (e.g. two different values of temperature difference associated with the same values of heat flux and wind speed). A quantitative analysis of this feature with a local equilibrium Reynolds-stress model is presented. The fixed-wind / fixed-shear maximum has been identified both in the bulk and in single-point flux–gradient relationships (that is, in the vertical temperature gradient and wind-shear parameter domain). The value of the Richardson number corresponding to this maximum is derived from the model equations. To study the possible feedback in strongly stable conditions, weak and intense cooling scenarios have been simulated with a one-dimensional numerical, high-resolution atmospheric boundary-layer model. Despite the rapid cooling, flow decoupling at the surface has not been observed; instead, a stability-limited heat flux is maintained, with a gradual increase of the Richardson number towards the top of the turbulent layer, with some signs of oscillatory behaviour at intermediate heights. Vertical changes of wind shear and the Brunt–Väisälä frequency display a remarkably non-monotonic character, with some signs of a gradually developing instability.     

非绝热加热对赤道地区平均纬向环流的作用——非线性响应

本文设计了一个两层非线性原始方程模式,做低谱展开,求出非线性方程组的解;讨论了在外参数变化情况下解及其相应环流的演变;并与线性响应作了对比。此外,还讨论了定常解的稳定性。 主要结论是:(1)非绝热加热各分量在非线性响应中能强迫出更为接近实际的赤道地区平均纬圈环流圈。(2)在非线性响应中,潜热加热对纬圈环流的作用是最主要的。随着外参数——湿度的变化,解出现突变现象,其对应的赤道地区平均纬圈环流从一个定常态变到另一个定常态;其中对流潜热的作用最为明显,感热加热的作用是次要的。(3)在非线性响应和线性响应中,辐射加热对环流的作用不同;潜热加热对环流的作用相似,但在前者中它要强得多。      

The three dimensional structure of the atmospheric energy budget: methodology and evaluation

Studies of the vertically-integrated energy and moisture budgets of the atmosphere are expanded to three dimensions. The vertical integrals of the moisture, energy and heat budget equations computed analytically act as a very strong constraint on any local computational results of the vertical structure. This paper focuses on the methodology and difficulties in closing the budgets and satisfying constraints, given the need to use a pressure coordinate because model coordinates all differ. Vertical interpolation destroys delicate mass balances and can lead to inconsistencies, such as from how geopotential or vertical motion is computed. Using the advective rather than flux form of the equations greatly reduces the contamination from these effects. Results are documented for January 1989 using European Centre for Medium Range Weather Forecasts reanalysis (ERA-40) data. The moistening, diabatic heating and total energy forcing of the atmosphere are computed as a residual from the analyses using the moisture, dry energy (dry static energy plus kinetic energy) and total atmospheric (moist static plus kinetic) energy equations. The components from the monthly averaged flow and transients, as a function of layer in the atmosphere, and as quasi-horizontal and vertical fluxes of dry static, latent and kinetic energy are examined. Results show the moistening of the atmosphere at the surface, its release as latent heat in precipitation and transformation into dry static energy, and thus net radiative cooling as a function of height and location. The vertically integrated forcings computed from the model parameterizations are compared with available observations and budget-derived values, and large ERA-40 model biases are revealed in radiation and precipitation. The energy and moisture budget-derived quantities are more realistic, although results depend on the quality of the analyses which are not constructed to conserve mass, moisture or energy, owing to analysis increments.     

An analytical study on the urban boundary layer

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Latent heat of melting and its importance for glaciation cycles

A dynamical energy balance model is developed including both latent heat and sensible heat exchanges. It is applied to reconstructing the history of the changes of the icesheet mass and the ocean surface temperature over an ice age. The zero-dimensional model is extended to include three-dimensional information of the icesheets by assuming a specific geometric shape of the icesheets. The ice-albedo feedback can then be calculated and, at the same time, the cryosphere interaction is introduced into the climate model. The advancing of the glaciers and the cooling of the oceans in a glacial period can be accounted for by the differential equations of the dynamic system if an external perturbation in the form of any energy deficit of 0.13% of the insolation is imposed. The earth orbital changes generate a heat deficit of this magnitude due to the change of the eccentricity and have the same periodicity of 100 000 years as the major glacial cycles. Therefore they could well be the origin of the Pleistocene ice ages. Editor's Note: This note generated strong, but mixed, reactions from three referees. Its conclusions should thus be weighed carefully. It is published despite the cautionary reviews in order to spur debate on the large remaining uncertainties over the causes of Pleistocene glacial cycles.     

A bulk model for the atmospheric planetary boundary layer

The integrated momentum and thermodynamic equations through the planetary boundary layer (PBL) are solved numerically to predict the mean changes of wind and potential temperature from which surface fluxes are computed using bulk transfer coefficients of momentum and heat. The second part of the study involves a formulation and testing of a PBL height model based on the turbulent energy budget equation where turbulent fluxes of wind and heat are considered as the source of energy. The model exhibits capability of predicting the PBL height development for both stable and unstable regimes of observed conditions. Results of the model agree favourably with those of Deardorff's (1974a) and Tennekes' (1973) models in convective conditions.Contribution number 396.     

Ocean Model Open Boundary Conditions with Volume,Heat and Salinity Conservation Constraints简

Open boundary conditions （OBCs） for a regional ocean model that can be integrated stably over a long timeframe, as well as satisfy the volume, heat and salinity conservation constraints, were developed. First, the idea that the inward and outward flux information can be treated separately in the OBCs was adopted. Second, in order to maintain the property that the volume, heat and salinity remains conserved in the simulation domain, conservation constraints were added to the OBCs, and an inverse method utilized to solve the constraint equations. Ideal experiments were designed to investigate the conservation property, and the OBCs were found to work efficiently to maintain the volume, heat and salinity conservation. It was found that simulations were comparable to observations when the OBCs were applied to a regional ocean model.