A model of airflow above changes in surface heat flux,temperature and roughness for neutral and unstable conditions

A numerical model of airflow in the lowest 50–100 m of the atmosphere above changes in surface roughness and temperature or heat flux has been developed based on boundary layer approximations, the Businger-Dyer hypotheses for the non-dimensional wind shear and heat flux and a mixing length hypothesis.Results have been obtained for several situations, in particular, airflow with neutral upstream conditions encountering a step change in surface temperature or heat flux with no roughness change. In these cases large increases in shear stress at the outer edge of the internal boundary layer are predicted. The case of unstable upstream flow encountering a step change to zero heat flux is also considered.Two situations that may be encountered near the shores of the Great Lakes are considered.Notation B Businger-Dyer constant (= 16.0) in form for _M, _H - c _p Specific heat at constant pressure - g Acceleration due to gravity - H Upward vertical heat flux - H ₀ , H ₁ Surface heat fluxes for x < 0, x 0 - k von Kármán's constant ( = 0.4) - l Mixing length - L Monin-Obukhov length - L ₀ Upstream value of L - m Ratio of roughness lengths (= z ₁/z ₀) - RL ^* Non-dimensional parameter, see Equations (20, 22 and 24) - RL ₁ ^* Same as RL ^* but with z ₁ scaling (= mRL ^*) - T Scaled temperature - T ₀ (z) Upstream temperature profile - u ₀, u ₁(x) Surface friction velocities for x < 0, x 0 - U, W Horizontal and vertical mean velocities - U ₀ (z) Upstream velocity profile - x, z Horizontal and vertical coordinates - z _i Local roughness length     

A study of abrupt climate change in a simple nonlinear climate model

We use a seasonal energy balance climate model to study the behavior of the snowline cycle as a function of external parameters such as the solar constant. Our studies are confined in this study to cases with zonally symmetric land-sea distributions (bands or caps of land). The model is nonlinear in that the seasonally varying snow/sea ice line modifies the energy receipt through its different albedo from open land or water. The repeating steady-state seasonal cycle of the model is solved by a truncated Fourier series in time. This method is several thousand times faster than a time stepping approach. The results are interesting in that a number of bifurcations in the snowline behavior are found and studied for various geographies. Polar land caps and land bands positioned near the poles exhibit a variety of discontinuous summer snow cover behaviors (abrupt transitions as a parameter such as solar constant is slowly varied), which may be relevant to the inception and decay of continental ice sheets.     

A simple model of baroclinic adjustment and parameterization of eddy heat transport

Summary A nonlinear, forced, dissipative quasi-geostrophic, two-level -plane model of baroclinic instability is formulated. The model resolves a baroclinic zonal flow and a wave of arbitrary zonal scale. Multiple equilibrium solutions describing Hadley and eddy circulations coexist. Only the circulation with smaller thermal wind is stable. The most efficient eddy activity occurs at a zonal wavenumber close to the wavelength of maximum instability of linear baroclinic instability theory. For a wide range of forcing and dissipative parameters, the steady baroclinic zonal wind of the eddy regime is close to the critical shear of linear theory. Eddy statistics are obtained analytically in terms of the doparture of the zonally symmetric state from radiative equilibrium. A parameterization for the eddy heat transport is obtained.With 14 Figures     

Wind profile and vertical motions above an abrupt change in surface roughness and temperature

A review is presented of some Russian-language papers published as early as 1952–1954 that are unknown to most English-speaking readers. In these papers the influence of an abrupt change in the surface friction velocityv _*, surface roughnessz ₀ and surface temperature or heat flux on the wind velocity profile and vertical motions has been investigated analytically and numerically. Most of the theories are based on the exchange-coefficient approximation for momentum and heat. In terms of this approximation, further generalization and development of the problem is discussed.In an appendix, the Shwetz method for approximate solution of the boundary-layer partial differential equations is briefly described, using as an example an equation for which an exact solution is also possible.     

Simple formulation of heat flux in the unstable atmospheric boundary layer

A formulation for the magnitude of the upward heat flux is developed for the common situation where information on temperature fluctuations is available but measurement of vertical motion fluctuations are unavailable or of inadequate quality. A relationship is also developed which allows inference of the vertical structure of the heat flux from the stability. This development uses data from the Air Mass Transformation Experiment and a number of existing studies in the literature.

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Résumé On établit ici une formulation du flux de chaleur ascendant dans le cas courant ou l'on dispose des fluctuations de température, tandis que les fluctuations du mouvement vertical ne sont pas disponibles ou sont de qualité inadéquate. On obtient également une relation qui permet de déduire la structure verticale du flux de chaleur à partir de la stabilité. Ce développement utilise les données de l'expérience Air Mass Transformation Experiment et plusieurs études existant dans la littérature.

     

干旱区热力学粗糙度特征及对感热通量估算的影响

利用ＨＥＩＦＥ的实测资料估算了黑河实验区几个沙漠戈壁表面上的热力学粗糙度（以附加阻尼ｋＢ＾－１的形式）,发现在任一测站ｋＢ＾－１值的变化范围较大,同时分析了附加阻尼项在估算感热通量时的作用,而忽略该附加阻尼将会导致对感热通量的明显高估,提出在利用阻尼型公式计算感热通量时,不能采用简单的ｚ０ｍ＝ｚ０ｈ的假设,否则会带来较大误差。     

Radiometrically determined skin temperature and scalar roughness to estimate surface heat flux part II: Performance of parameterized scalar roughness for the determination of sensible heat

Several formulations and proposals to determine the value of the radiometric scalar roughness for sensible heatz _0h,r are tested with respect to their performance in the estimation of the sensible heat flux by means of the profile equations derived from Monin-Obukhov similarity theory. The equations are applied to the data set of spatially averaged surface skin temperature and profiles of wind speed and temperature observed in a pasture field during a growing season. The use of a physical model developed for a dense canopy to estimate scalar roughness for sensible heatz _0h,r produced sensible heat fluxH with a correlation coefficientr=0.884, the ratio of means being H _s /H=1.19 in a comparison with reference values ofH _s . In comparison, a proposal for a fixed value ofz _0h yieldedr=0.887, H _s /H=0.879. In both cases, the validity ofz _0h =z _0h,r was assumed. All expressions derived to estimatez _0h,r from a multiple linear regression with such predictors as leaf area index, solar radiation and the ratio of solar radiation to extraterrestrial radiation, were found to produce a better result, withr better than 0.90 and H _s /H around 1.0. However, when the constantsc andf of a linear regression equationHs=cH+f are used to evaluate the equations, a marked difference in performance of each formulation appeared. In general, equations with smaller numbers of predictors tend to produce a biased result, i.e., an overestimation ofH at largeH _s . These values ofH are used in conjunction with the energy balance equation to derive values of the latent heat fluxLE, which are shown to be in good agreement with the reference valuesLE _s , withr greater than 0.97.     

Airflow above changes in surface heat flux,temperature and roughness; an extension to include the stable case

A numerical model of airflow above changes in surface roughness and thermal conditions is extended to include cases with stable thermal stratification within the internal boundary-layer. The model uses a mixing-length approach with empirical forms for M and H.Results are presented for some basic cases and an attempt is then made to compare results given by the model with the experimental results of Rider, Philip and Bradley. Tolerable agreement is achieved. The importance of roughness change and thermal stability effects in the diffusion of heat and moisture near a leading edge is emphasised.Notation A Refers to Taylor (1970) - B Businger-Dyer constant (= 16.0) in forms for _M and _H - C Constant in form for in stable case - c _p Specific heat at constant pressure - E Scaled absolute humidity - g Acceleration due to gravity - H Upward vertical heat flux - H ₀, H ₁ Surface heat fluxes for x <0, x0 - H _E Upward latent heat flux - k Von Kármán's constant (= 0.4) - K _H K _W Eddy transfer coefficients for heat and water vapour - L Monin-Obukhov length - L _H Latent heat of evaporation for water - m Ratio of roughness lengths ( = z ₁/z ₀) - RPB Refers to Rider et al. (1964) - RL* Non-dimensional parameter (see Equations (9), (20a), (22a), (24a)) - R* Net radiation less ground heat flux (see Equations (15), (16)) - T Scaled temperature - T ₁ Downstream scaled surface temperature - u ₀ u ₁(x) Surface friction velocities for x <0, x0 - U, W Horizontal and vertical mean velocities - x, z Horizontal and vertical co-ordinates - Z _i Local roughness length - z ₀, z _i Roughness lengths for x < 0, x 0 - Temperature - ₀, ₁ Surface temperatures for x<0, x0 - _E Non-dimensional absolute humidity gradient - _H Non-dimensional temperature gradient of heat flux - _M Non-dimensional wind shear - = _M = _H = _E an assumption used in stable conditions - Air density - Absolute humidity - _w Density of water - Kinematic shear stress - Logarithmic height scale (= ln(z+z ₁)/z ₁)     

Estimation of the average surface heat flux over an inhomogeneous terrain from the vertical velocity variance

An indirect method of estimating the surface heat flux from observations of vertical velocity variance at the lower mid-levels of the convective atmospheric boundary layer is described. Comparison of surface heat flux estimates with those from boundary-layer heating rates is good, and this method seems to be especially suitable for inhomogeneous terrain for which the surface-layer profile method cannot be used.     

A simple unified theory for flow in the canopy and roughness sublayer

The mean flow profile within and above a tall canopy is well known to violate the standard boundary-layer flux–gradient relationships. Here we present a theory for the flow profile that is comprised of a canopy model coupled to a modified surface-layer model. The coupling between the two components and the modifications to the surface-layer profiles are formulated through the mixing layer analogy for the flow at a canopy top. This analogy provides an additional length scale—the vorticity thickness—upon which the flow just above the canopy, within the so-called roughness sublayer, depends. A natural form for the vertical profiles within the roughness sublayer follows that overcomes problems with many earlier forms in the literature. Predictions of the mean flow profiles are shown to match observations over a range of canopy types and stabilities. The unified theory predicts that key parameters, such as the displacement height and roughness length, have a significant dependence on the boundary-layer stability. Assuming one of these parameters a priori leads to the incorrect variation with stability of the others and incorrect predictions of the mean wind speed profile. The roughness sublayer has a greater impact on the mean wind speed in stable than unstable conditions. The presence of a roughness sublayer also allows the surface to exert a greater drag on the boundary layer for an equivalent value of the near-surface wind speed than would otherwise occur. This characteristic would alter predictions of the evolution of the boundary layer and surface states if included within numerical weather prediction models.     

A model for Dansgaard–Oeschger events and millennial-scale abrupt climate change without external forcing

Climate Dynamics - We propose a conceptual model which generates abrupt climate changes akin to Dansgaard–Oeschger events. In the model these abrupt climate changes are not triggered by...     

A model for sensible heat flux probability density function for near-neutral and slightly-stable atmospheric flows

The probability density function for sensible heat flux was measured above a uniform dry lakebed (Owens lake) in Owens Valley, California. It was found that for moderately stable to near neutral atmospheric stability conditions, the probability density function exhibits well defined exponential tails. These exponential tails are consistent with many laboratory boundarylayer measurements and numerical simulations. A model for the sensible heat flux probability density function was developed and tested. A key assumption in the model derivation was the near Gaussian statistics of the vertical velocity and temperature fluctuations. This assumption was verified from time series measurements of temperature and vertical velocity. The parameters for the sensible heat flux probability density function model were also derived from mean meteorological and surface conditions using surface-layer similarity theory. It was found that the best agreement between modeled and measured sensible heat flux probability density function was at the tails. Finally, a relation between the intermittency parameter, the probability density function, and the mean meteorological conditions was derived. This relation rigorously links the intermittency parameter to mean meteorological conditions.     

An empirical method for demonstrating the influence of heat flux on the shape of temperature spectra

An empirical method is presented which demonstrates the influence of heat flux on the shape of the temperature spectrum within the frequency interval associated with the majority of temperature-variance production. The method is tested on temperature spectra obtained over corn (Zea mays [L.]) and red pine (Pinus resinosa [Ait.]) surfaces with reasonably good results.     

A simple model for potential dewfall in an arid region

It is not always easy to know, post-facto, whether both dewfall and fog may have occurred over a given evening period. Instrumentation limitations make it difficult to quantify dew deposition since they rely on artificial sensing surfaces that are either visually examined on a daily basis or recorded. In arid to Mediterranean regions, both dew and fog can play significant ecological roles as suppliers of moisture. Long-term observation records of dew and fog in such regions tend to be limited, however, due partly to a lack of interest and limited distribution of well-instrumented meteorological stations. Simple meteorological criteria are suggested here to calculate potential dewfall and to indicate whether fog was likely to have occurred over a given evening. A field campaign was carried out in the NW Negev desert, Israel, in September and October 1997, to collect meteorological data and carry out dewfall measurements.     

A simple yet more accurate model to calculate solar radiative flux in the inhomogeneous atmosphere

A simple yet more accurate semiempirical model is developed to calculate solar radiative flux in the optically inhomogeneous atmosphere. In the model a parameterized expression of spherical reflectance and transmitance of the atmosphere is confirmed, and the weighted single scatter albedo and weighted asymmetric factor are introduced to fit four empirical correction factors responsible for radiative fluxes in the inhomogeneous atmosphere. For both clean and turbid models, there are 120060 sets of radiative flux simulations for accuracy checks of the model, which cover 0-50 cloud optical depths, 0-0.8 surface reflectance, Junge and Log-normal aerosol size distributions, and 0-0.05 imaginary parts of aerosol refractive indexes. In case of the homogeneous atmosphere, standard errors of the 120060 upward fluxes from the present model are 1.08% and 1.04% for clean and turbid aerosol models, respectively; and those of the downward fluxes are 4.12% and 3.31%. In case of the inhomogeneous atmosphere, standard errors of the upw ard fluxes from the present model are 3.01% and 3.48% for clean and turbid aerosol models.respectively; and those of the downward fluxes are 4.54% and 4.89%, showing a much better accuracy than the results calculated by using an assumption of the homogeneous atmosphere.     

百年来上海、北京气候突变的初步分析

本文应用Mann-Kendall方法对1873—1989年上海、北京的气温、降水时间序列进行了突变检验。其结果表明,上海、北京的百年气温分别在1932年和1919年出现冷转暖的气候突变。同时,还判别出上海降水在1906年发生突变,其后进入一个相对多雨时段。北京降水突变在1903年,而后进入一个相对少雨时段。另外,还用其它方法对突变点加以验证说明。     

Uncoupled multi-layer model for the transfer of sensible and latent heat flux densities from vegetation

The sensible heat flux density C and the latent heat flux density E are coupled in the case of a multi-layer model of vegetation. Therefore two linearly independent combinations of C and E, the enthalpy flux density H and the saturation heat flux density J, are introduced. Two electrical analogues, for H and J, are designed. They are equivalent to the resistance scheme for C and E, but uncoupled. Penman's formulas for C and E, which are applicable only to single-layer models, can be expressed equivalently in terms of H and J. This version of Penman's formulas can be extended easily to multi-layer canopies.     

A study of long-term climate change in a simple seasonal nonlinear climate model

Solar radiation cycles, earth-orbital changes, and continental drift drive long to very long term (10³–10⁶ years) climatic changes. Lin and North used the stationary solutions of a simple energy balance model (EBM) to study the equilibrium climatic stages. In this paper, we study time dependent solutions and, in particular, transition processes. We make use of two time scales: a seasonal cycle (fast variation) and a long term time change (slow variation). Variations over short time scales are solved using a Fourier transform in time and long term variations are studied using a 4th order Runge-Kutta method. The energy balance equation is a parabolic type equation and it is well posed. Climate changes depend mainly on external forcing and the state of the climate is determined by the slow time scale forcing. In other words, transitions from one climate stage (snow-covered) to another (snow-free) at bifurcation points are monotonic, despite 20% to 50% shortperiod random fluctuations in the solar energy. This smooth transition is especially noticeable when the land bands lie close to the north pole (70° N to 90° N) or at high latitudes (50° N to 75° N).Now at Applied Physics Laboratory, The Johns Hopkins University, Laurel, MD 20723, USA     

A simple model for describing the heat balance of a shallow lake with application to Lake Chad

A model is described allowing the computation of a shallow lake's surface temperature as a function of the meteorological conditions of the surroundings. An equilibrium temperature with no heat flux through the surface is defined. The daily cycle of the equilibrium temperature permits computation of the average and the amplitude of the lake's temperature in the form of a simple sine wave. The computed values are compared with satellite measurements of the surface temperature and good agreement is achieved. When the computed surface temperature is applied, the values of the fluxes of latent and sensible heat are in good agreement with observational data.