Estimation of the Exchange Coefficient of Heat During Low Wind Convective Conditions

For the first time, the exchange coefficient of heat C_H has been estimated from eddy correlation of velocity and virtual temperature fluctuations using sonic anemometer measurements made at low wind speeds over the monsoon land atJodhpur (26°18' N, 73°04' E), a semi arid station. It shows strong dependence on wind speed, increasing rapidly with decreasing wind speed, and scales according to a power law C_H = 0.025U₁₀ ^-0.7 (where U₁₀ is the mean wind speed at 10-m height). A similar but more rapid increase in the drag coefficient C_Dhas already been reported in an earlier study. Low winds (<4 m s^-1) are associated with both near neutral and strong unstable situations. It is noted that C_H increases with increasing instability. The present observations best describe a low wind convective regime as revealed in the scaling behaviour of drag, sensible heat flux and the non-dimensional temperature gradient. Neutral drag and heat cofficients,corrected using Monin–Obukhov (M–O) theory, show a more uniform behaviour at low wind speeds in convective conditions, when compared with the observed coefficients discussed in a coming paper.At low wind convective conditions, M-O theory is unable to capture the observed linear dependence of drag on wind speed, unlike during forced convections. The non-dimensional shear inferred from the present data shows noticeable deviations from Businger's formulation, a forced convection similarity. Heat flux is insensitive to drag associated with weak winds superposed on true free convection. With heat flux as the primary variable, definition of new velocity scales leads to a new drag parameterization scheme at low wind speeds during convective conditionsdiscussed in a coming paper.     

Air-sea bulk transfer coefficients in diabatic conditions

On the basis of recent data for the roughness Reynolds number of the sea surface, and using the Owen-Thomson theory on the transfers of heat and mass between a rough surface and the flow above it, the bulk transfer coefficients of the sea surface have been estimated. For a reference height of 10 m, the neutral-lapse transfer coefficient for water vapor is larger by only a few percent than that for sensible heat. When the wind speed at the 10-m height is u ₁₀>3 m s^–1, the coefficient for sensible heat C _H is larger by about 10% than that for momentum C _D . For u ₁₀<5 m s^–1, however, the value of C _D exceeds the value of C _H , and for u ₁₀=15 m s^–1 it is shown that C _H 0.8C _D . It may be also proposed that 10³ C _D =1.11 to 1.70, 10³ C _E =1.18 to 1.30, and 10³ C _H =1.15 to 1.26 for a range of u ₁₀=4 to 20 m s^–1. A plot of diabatic transfer coefficients versus wind speed is obtained by using a parameter of the sea-air temperature difference. For practical purposes, the coefficients are approximated by empirical formulae.     

A theory for the scalar roughness and the scalar transfer coefficients over snow and sea ice

Although the bulk aerodynamic transfer coefficients for sensible (C _H ) and latent (C _E ) heat over snow and sea ice surfaces are necessary for accurately modeling the surface energy budget, they have been measured rarely. This paper, therefore, presents a theoretical model that predicts neutral-stability values of C _H and C _E as functions of the wind speed and a surface roughness parameter. The crux of the model is establishing the interfacial sublayer profiles of the scalars, temperature and water vapor, over aerodynamically smooth and rough surfaces on the basis of a surface-renewal model in which turbulent eddies continually scour the surface, transferring scalar contaminants across the interface by molecular diffusion. Matching these interfacial sublayer profiles with the semi-logarithmic inertial sublayer profiles yields the roughness lengths for temperature and water vapor. When coupled with a model for the drag coefficient over snow and sea ice based on actual measurements, these roughness lengths lead to the transfer coefficients. C _E is always a few percent larger than CH. Both decrease monotonically with increasing wind speed for speeds above 1 m s^–1, and both increase at all wind speeds as the surface gets rougher. Both, nevertheless, are almost always between 1.0 × 10^–3 and 1.5 × 10^–3.     

Heat energy exchange over a large water body under stable atmospheric conditions

The surface heat budget over the Riband reservoir covering 300 km² is investigated making use of hydrometeorological data collected at a number of stations during May and June 1983. The observations had to be restricted to 0800–1400 hr for operational reasons in this remote part of India. The winds were weaker, and in general the temperature and humidity gradients were stronger at that time of day than during the afternoon.The mean albedo between 0700–1200 hr is found to be about 34% which could be due to the high turbidity of the water. A simple relation of the form, R = (1 – )Q _i – 85 is proposed to estimate net radiation over the water body from the global radiation. This relation is useful for the computation of net radiation since it avoids the computation of effective back radiation, which requires data on humidity, cloud amount and surface water temperature. The overall means of net radiation, latent and sensible heat fluxes were found to be 420, 96 and -11 W/m², respectively. A net heat gain of about 335 W/m² was observed during the study period. The measured effective back radiation agreed reasonably well with the value computed from the theoretical formula.     

Thermal effect of the sea breeze on the structure of the boundary layer and the heat budget over land

The daytime boundary-layer heating process and the air-land heat budget were investigated over the coastal sea-breeze region by means of observations over the Sendai plain in Japan during the summer. In this area, the onset of the sea breeze begins at the coast around 0900 LST, intruding about 35 km inland by late afternoon. The cold sea breeze creates a temperature difference of over 10°C between the coastal and inland areas in the afternoon. On the other hand, warm air advection due to the combination of the counter-sea breeze and land-to-sea synoptic wind occurs in the layer above the cold sea breeze in the coastal region. Owing to this local warm air advection, there is no significant difference in the daytime heating rate over the entire atmospheric boundary layer between the coastal and inland areas. The sensible heat flux from the land surface gradually decreases as distance from the coastline increases, being mainly attributed to the cold sea breeze. The daytime mean cold air advection due to the sea breeze is estimated asQ _adv ^local =–29 W m^–2 averaged over the sea breeze region (035 km from the coastline). This value is 17% of the surface sensible heat fluxH over the same region. The results of a two-dimensional numerical model show that the value ofQ _adv ^local /H is strongly affected by the upper-level synoptic wind direction. The absolute value ofQ _adv ^local /H becomes smaller when the synoptic wind has the opposite direction of the sea breeze. This condition occurred during the observations used in the present study.     

The distribution of solar radiation over the Earth's surface

Summary Records of total solar radiation measured on a horizontal surface (Q) on a monthly basis and of more than three years' duration are available for 88 stations. The stations are mainly concentrated in North America and Europe, and it is not possible to determine the global distribution of radiation directly from these records. Solar radiation and mean cloud amount (C) were therefore related by the quadratic regressionQ=Q _A (0.803–0.340C–0.458C ²), whereQ _A is the maximum possible radiation in the absence of an atmosphere (Angot's values) and the values ofC were obtained from the maps printed inShaw's Manual of Meteorology.Using the known distribution ofQ _A andC, values ofQ were calculated by use of the equation above for each 5° intersection of latitude and longitude over land, and for each 10° intersection over sea. Isopleths ofQ for each successive 50 gcal/cm² day are shown on the 12 monthly maps on which the distribution of radiation over the earth's surface is illustrated. Attention is drawn to certain features of these maps, in particular to the occurrence and movement of zones of high radiation, and a comparison is made of estimated and recorded radiation for twelve stations.

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Zusammenfassung Registrierungen der Monatswerte der Globalstrahlung auf Horizontalfläche (Q) über mindestens drei Jahre liegen für 88 Stationen vor; diese sind vorwiegend auf Nordamerika und Europa konzentriert, und es ist daher nicht möglich, auf Grund davon die gesamte Strahlungsverteilung über die Erde zu bestimmen. Es wird nun mit Hilfe der quadratischen RegressionsgleichungQ=Q _A (0.803–0.340C–0.458C ²) eine Beziehung zwischen GlobalstrahlungQ und mittlerer BewölkungC aufgestellt, woQ _A den Maximalwert der Globalstrahlung bei Fehlen einer Atmosphäre bedeutet und die Konstanten nachAngot und die Bewölkungsdaten nachShaw angenommen sind.Auf Grund der Verteilung vonQ _A undC wurden mit Hilfe der angegebenen Gleichung für jeden Bereich von je 5° Länge und Breite über Land von je 10° über Meer die Werte der Globalstrahlung berechnet. Isoplethen der Globalstrahlung für Stufen von je 20 gcal/cm² Tag sind in 12 Monatskarten wiedergegeben, auf denen die Strahlungsverteilung über die Erde dargestellt ist. Einige Resultate dieser Karten werden besprochen, im speziellen das Auftreten und die Verschiebung der Zonen hoher Strahlung; zudem wird für 12 Stationen eine Vergleichung zwischen der berechneten und der registrierten Strahlung durchgeführt.

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Résumé On possède des enregistrements de 88 stations pour les sommes mensuelles du rayonnement global sur une surface horizontale (Q) pour des périodes d'au moins 3 ans. Ces stations sont concentrées essentiellement en Amérique du Nord et en Europe ce qui ne permet pas d'en déduire la répartition du rayonnement global sur toute la terre. Pour cette raison l'auteur établit, au moyen de l'équation carrée de régressionQ=Q _A (0.803–0.340C–0.458C ²), une relation entre le rayonnement globalQ et la moyenne de la nébulositéC, oùQ _A représente la valeur maximale du rayonnement global sans atmosphère et où les constantes sont données selonAngot, la nébulosité selonShaw.A partir de la répartition deQ et deC et à l'aide de la formule précédente l'auteur a calculé les valeurs du rayonnement global pour des surfaces de 5° de latitude et de longitude sur terre et de 10° sur mer. Des isoplèthes représentent le rayonnement global par échelons de 50 gcal/cm² jour, sur 12 cartes mensuelles qui illustrent sa répartition sur toute la terre. L'auteur discute encore divers résultats de ces cartes, en particulier l'apparition et le déplacement des zones de fort rayonnement, et compare encore pour 12 stations les résultats obtenus par le calcul et par enregistrement.

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With 14 Figures     

卫星遥感结合气象资料计算的青藏高原地面感热特征分析

本文选取1981年7月至2012年12月美国国家航空和航天局（NASA）制作的归一化的动态植被指数（NDVI）资料、根据NDVI值计算地表热力输送系数（C_H）的参数化关系式（C_H-I_NDV）和青藏高原70个常规气象观测资料,计算了青藏高原全区的逐月地表热力输送系数（C_H）,讨论了其时空分布特征,并在此基础上计算了高原70个常规台站的感热通量（SSHF）序列,并与已有感热资料进行了对比。随后,探讨了地面感热通量的气候特征及其年际变化与气候因子的关系。结果表明:高原地区的C_H值具有明显的空间差异和季节差异,表现为东高西低、夏季大、冬季小的特点。感热的年际变化在冬季主要响应于地气温差的变化,夏季则受地面风速影响较大;由于风速减小趋缓,地气温差增大,变化趋势在2003年前后由减弱趋势转变为增强趋势,这种趋势的转变最早发生在2001年秋季,且在高原全区具有较好的一致性。     

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.Symbols c entrainment parameter for sensible heat - c _p specific heat of air at constant pressure, 1010 J kg^–1 K^–1 - d ₁ the thickness of velocity shear at the mixed-layer top, m - Q _H surface sensible heat flux, W m^–2 - u _m mean mixed-layer wind speed, m s^–1 - u _* friction velocity at the surface, m s^–1 - w subsidence velocity, m s^–1 - W subsidence warming,^oC s^–1 - w _e entrainment velocity, m s^–1 - w _* convection velocity in the mixed layer, m s^–1 - x downwind horizontal distance from the water-land interface, m - y dummy variable forx, m - Z height above the surface, m - Z _i height of capping inversion, m - Z _m mixed-layer depth, i.e.,Z _i–Z_s, m - Z _s height of the surface layer, m - lapse rate of potential temperature aboveZ _i, K m^–1 - potential temperature step atZ _i, K - u _h velocity step change at the mixed-layer top - _m mean mixed-layer potential temperature, K     

Characteristics of atmospheric turbulence in the surface layer over Antarctica

This paper presents meteorological measurements made during the antarctic summer period, on two 9 m and 3 m towers, on the rocky and ice shelf terrains of the Indian antarctic stations Maitri and Dakshin Gangotri, respectively. The measurements of fluctuations in temperature and wind speed made with relatively lesser precision instrumentation pertain to smaller wave numbers ~10^-2 m^-1 appropriate to outer scale L ₀ of the atmospheric turbulence spectrum. Autocorrelation analysis of the fluctuations in temperature and wind speed has been performed. A new autoregressive scheme has been developed to represent the computed autocorrelation functions by a Yule statistical model, and to estimate the correlation period T ₀ of the turbulent medium. Height profiles of outer scale L ₀ of turbulence may be given in terms of T ₀ and mean wind speed u. Further, the similarity theory of Monin-Obukhov has been used to compute height profiles of temperature structure parameter C _T ². At Maitri, values of L ₀ and C _T ² are higher between 03–22 h local time than between 22–03 h. Values of L ₀ and C _T ² are smaller over the ice shelf terrain of the Dakshin Gangotri station, compared to those over the rocky terrain of the Maitri station.     

Momentum and scalar transfer coefficients over aerodynamically smooth antarctic surfaces

Vertical profiles of wind speed, temperature and humidity were used to estimate the roughness lengths for momentum (z ₀), heat (z _H ) and moisture (z _Q) over smooth ice and snow surfaces. The profile-measurements were performed in the vicinity of a blue ice field in Queen Maud Land, East Antarctica. The values ofz ₀ over ice (3·10^–6 m) seem to be the smallest ever obtained over permanent, natural surfaces. The settling of snow on the ice and the loss of momentum at saltating snow particles serve as momentum dissipating processes during snow-drift events, expressed as a strong dependence ofz ₀ on u_#.The scalar roughness lengths and surface temperature can be evaluated from the temperature and humidity profile measurements if the ratioz _H /z _Q is specified. This new method circumvents the difficult measurement of surface temperature. The scalar roughness lengths seem to be approximately equal toz0 for a large range of low roughness Reynolds numbers, despite the frequent occurrence of drifting snow. Possible reasons for this agreement with theory of non-saltating flow are discussed.     

The dependence of the measured cool skin of the ocean on wind stress and total heat flux

The temperature drop T between the ocean surface and the 5-cm depth was recorded during GATE, Phase III. With measured values of the total heat flux Q and an assumption about the thickness of the viscous boundary layer of the ocean, the wind-speed dependence of the factor of proportionality between T and Q is determined. This factor depends on the deviations of the thickness of the conductive layer from the thickness of the viscous layer and possibly partially on the wind stress. A further assumption about the thickness of the conductive layer leads to a wind-speed dependence of the ratio between total wind stress and its wave supporting part of it. This ratio increases from a value 1.5 at 1 m s^–1 to 9 at 10 m s^–1, which is in agreement with existing estimates.     

Models for estimating offshore winds from onshore meteorological measurements

To understand and estimate wind speed differences across the coastal zone, two models, one theoretical and another semi-empirical, have been developed and verified by available data sets. Assuming that: (1) mean horizontal motion exists across the coastal zone; and (2) the geostrophic wind does not change appreciably at the top of the planetary boundary layer (PBL), the equation of motion in the direction of the wind can be reduced so that 341-01, where U, H, and C _D are wind speed, height of PBL, and drag coefficient over the sea and land, respectively. For practice, C _D SEA has been modified from a formula with U _LAND as the only input. H _SEA may be estimated routinely from known H _{D LAND LAND} and the temperature difference between land and sea, which can be provided by such means as remote sensing from meteorological satellites. For a given coast, Cmay be estimated also. This formula is recommended for weather forecasters. The semiempirical formula is based mainly on the power law wind distribution with height in the PBL. The formula states that 341-02. Simultaneous offshore and onshore wind measurements made at stations ranging from Somalia, near the equator, to the Gulf of Alaska indicated that values of a and b are 2.98 and 0.34 with a correlation coefficient of -0.95. For oceanographic applications, a simplified equation, i.e., 341-03, is also proposed.     

珠海凤凰山森林下垫面干季和湿季气象要素的对比分析与动量和感热交换系数的参数化研究

利用珠海凤凰山陆气相互作用观测塔站2014年11月至2016年5月的观测数据,对比分析了干湿季森林下垫面能量通量和气象要素的变化特征,分析了在不同稳定度下3个风向范围（315°～45°、45°～135°和135°～225°）的动量和感热交换系数随冠层表面风速的变化特征,并对动量和感热交换系数进行了参数化研究。结果表明:干季感热和潜热通量值相当,湿季潜热远大于感热。干季和湿季的夜晚都出现负感热现象,感热从大气向森林输送。相对湿度的变化幅度大,与该地气象状况密切相关,相对湿度的垂直梯度夜晚较大,白天较小。干季的气温垂直梯度比湿季的明显。风速在冬季变化平缓,夏季变化剧烈,低层风速随高度变化梯度明显,高层较紊乱。各高度风向差异不大。中性和近中性状态下,在风向为315°～45°、45°～135°和135°～225°时,动量交换系数C_dn分别为0.05、0.0055和0.022,感热交换系数C_hn分别为0.0055、0.003和0.004。在稳定和不稳定状态下,动量交换系数C_d、感热交换系数C_h随冠层表面风速v明显发生变化,稳定条件下,C_d、C_h随v的增大而增大;不稳定条件下,C_d、C_h随v的增大而减小。分不同风向对森林冠层C_d、C_h在稳定和不稳定条件下与v的关系进行了拟合,得到了参数化公式。     

Henry's law coefficients for aqueous solutions of acetone,acetaldehyde and acetonitrile,and equilibrium constants for the addition compounds of acetone and acetaldehyde with bisulfite

Vapor phase concentrations of acetone, acetaldehyde and acetonitrile over their aqueous solutions were measured to determine Henry's law partition coefficients for these compounds in the temperature range 5–40 °C. The results are for acetone: ln(H ₁/atm)=–(5286±100)T+(18.4±0.3); acetaldehyde: ln(H ₁/atm)=–(5671±22)/T+(20.4±0.1); and acetonitrile: ln(H ₁/atm)=–(4106±101)/T+(13.8±0.3). Artificial seawater of 3.5% salinity in place of deiionized water raisesH ₁ by about 15%. A similar technique has been used to measure the equilibrium constants for the addition compounds of acetone and acetaldehyde with bisulfite in aqueous solution. The results are ln(K ₁/M ^–1)=(4972±318)/T–(11.2±1.1) and ln(K ₁/M ^–1)=(6240±427)/T–(8.1±1.3), respectively. The results are compared and partly combined with other data in the literature to provide an average representation.     

Momentum and sensible heat fluxes calculated by the dissipation technique during the Ocean Storms Project

High frequency measurements of wind velocity and temperature were made during the Ocean Storms Project in November 1987. The dissipation method was applied to the resulting time series in order to determine friction velocities,u _*, and the characteristic temperature scale,t _*, at 1-min intervals. These values were then compared to the 1-min mean wind speed and air-sea temperature differences to determine relationships for the drag coefficient (C _d ) and Stanton number (C _h ). The drag coefficient was comparable to other values reported in the literature, although the variation with wind speed was greater than reported by other investigators. An examination of the residual time series indicated a systematic low frequency periodicity of about 2-hr duration which was attributed to a fluctuating wind interacting with the surface gravity wave field. The temperature fluctuations did not produce meaningful estimates ofC _h for stable conditions. For unstable conditions, a value of 1.09±0.02×10^–3 was found.     

Approximation formulas for the microphysical properties of saline droplets

Microphysical theory has proven essential for explaining sea spray's role in transferring heat and moisture across the air–sea interface. But large-scale models of air–sea interaction, among other applications, cannot afford full microphysical modules for computing spray droplet evolution and, thus, how rapidly these droplets exchange heat and moisture with their environment. Fortunately, because the temperature and radius of saline droplets evolve almost exponentially when properly scaled, it is possible to approximate a droplet's evolution with just four microphysical endpoints: its equilibrium temperature, T_eq; the e-folding time to reach that temperature, τ_T; its equilibrium radius, r_eq; and the e-folding time to reach that radius, τ_r.Starting with microphysical theory, this paper derives quick approximation formulas for these microphysical quantities. These approximations are capable of treating saline droplets with initial radii between 0.5 and 500 μm that evolve under the following ambient conditions: initial droplet temperatures and air temperatures between 0 and 40 °C, ambient relative humidities between 75% and 99.5%, and initial droplet salinities between 1 and 40 psu.Estimating T_eq, τ_T, and τ_r requires only one-step calculations; finding r_eq is done recursively using Newton's method. The approximations for T_eq and τ_T are quite good when compared to similar quantities derived from a full microphysical model; T_eq is accurate to within 0.02 °C, and τ_T is typically accurate to within 5%. The estimate for equilibrium radius r_eq is also usually within 5% of the radius simulated with the full microphysical model. Finally, the estimate of radius e-folding time τ_r is accurate to within about 10% for typical oceanic conditions.     

Solubility of HOCl in water and aqueous H2SO4 to stratospheric temperatures

Henry's law constants K_H (mol kg^–1 atm^–1) for the reaction HOCl_(g)=HOCl_(aq) near room temperature, literature data for the associated enthalpy change, and solubilities of HOCl in aqueous H₂SO₄ (46 to 60 wt%) at temperatures relevant to the stratosphere (200 KT230 K) are shown to be thermodynamically consistent. Effective Henry's law constants [H*=mHOCl/pHOCl, in mol kg^–1 atm^–1] of HOCl in aqueous H₂SO₄ are given by: ln(H*)=6.4946–mH₂SO₄(–0.04107+54.56/T)–5862 (1/T_o–1/T) where T(K) is temperature and T_o=298.15K. The activity coefficient of HOCl in aqueous H₂SO₄ has a simple Setchenow-type dependence upon H₂SO₄ molality.     

Three-dimensional modeling of synthetic cold fronts approaching the Alps

Summary A numerical model was used to study the behaviour of prototype cold fronts as they approach the Alps. Two fronts with different orientations relative to the Alpine range have been considered. One front approaches from west, a second one from northwest. The first front is connected with southwesterly large-scale air-flow producing pre-frontal foehn, whereas the second front is associated with westerly largescale flow leading to weak blocking north of the Alps.Model simulations with fully represented orography and parameterized water phase conversions have been compared with control runs where either the orography was cut off or the phase conversions were omitted. The results show a strong orographic influence in case of pre-frontal foehn which warms the pre-frontal air and increases the cross-frontal temperature contrast leading to an acceleration of the front along the northern Alpine rim. The latent heat effect was found to depend much on the position of precipitation relative to the surface front line. In case of pre-frontal foehn precipitation only falls behind the surface front line into the intruding cold air where it partly evaporates. In contrary, precipitation already appears ahead of the front in the case of blocking. Thus, the cooling effect of evaporating rain increases the cross-frontal temperature difference only in the first case causing an additional acceleration of the front.List of symbols C _pd specific heat capacity of dry air at constant pressure (C _pd =1004.71 J kg^–1 K^–1) - C _pv specific heat capacity of water vapour at constant pressure (C _pv =1845.96 J kg^–1 K^–1) - C _f propagation speed of a front - x, y horizontal grid spacing (cartesian system) - , horizontal grid spacing (geographic system) - t time step - E turbulent kinetic energy - f Coriolis parameter - g gravity acceleration (g=9.81 ms^–1) - h terrain elevation - H height of model lid (H=9000 m) - k Karman constant (k=0.4) - K _Mh horizontal exchange coefficient of momentum - K _Hh horizontal exchange coefficient of heat and moisture - K _Mz vertical exchange coefficient of momentum - K _Hz vertical exchange coefficient of heat and moisture - l mixing length - l _c specific condensation heat (l _c =2500.61 kJ kg^–1) - l _f specific freezing heat (l _f =333.56 kJ kg^–1) - l _s specific sublimation heat (l _s =2834.17 kJ kg^–1) - longitude - m ₁,m ₂,m ₃ metric coefficients - p pressure - Exner function - Pr Prandtl number - latitude - _M profile function - q _v specific humidity - q _c specific content of cloud droplets - q _i specific content of cloud ice particles - q _R specific content of rain drops - q _S specific content of snow - R _d gas constant of dry air (R _d =287.06 J kg^–1 K^–1) - R _v gas constant of water vapour (R _v =461.51 J kg^–1 K^–1) - r _E radius of earth (r _E =6371 km) - Ri _F flux Richardson number - density of dry air - t time - T temperature - _dia period of diastrophy - potential temperature - _v virtual potential temperature - _e equivalent potential temperature - U relative humidity - u, v, w cartesian wind components - u _F ,v _F front-normal and front-parallel wind components - x, y, z cartesian coordinates - w ^* transformed vertical wind component - W _R speed of falling rain - W _S speed of falling snow - z ^* transformed vertical coordinate Abbreviations GND (above) ground level - MSL (above) mean sea level With 12 Figures     

An analytical exericise to elucidate quasi-geostrophic frontogenesis

Summary Frontogenesis is frequently described by theQ-vector (Hoskins et al., 1978), a term being composed of several derivatives of basic meteorological parameters and their products. Its distribution and especially the _H ·Q-fields are highly important to estimate frontogenesis and cross frontal circulation. Although theQ-vector (Hoskins et al., 1978) allows an easier assessment of the vertical wind forcing than the original omega equation of the quasi-geostrophic theory, it is still difficul to imagine the three-dimensional (3-d) spatial distribution ofQ and _H ·Q even for standard atmospheric fields. Thus there is a need to shed more light in theQ and _H ·Q-fields for special synoptic situations.This is done here by constructing analytical 3-d geostrophically balanced wind-and temperature fields, for which theQ-forcing (Qformed with the geostrophic wind) can easily be computed and presented. Three examples (see Sections 3 to 5) are discussed yielding typical and realistic (compared to known pattern) 3-d forcing distributions ofQ and _H ·Q. Within the simple analytical scheme used here their origin can casily be understood. These fields of a 2000×2000 km² horizontal domain ranging up to 250 hPa are: A modified Bergeron deformation field containing a cold front (case I a) and a warm front (case I b); an upper tropospheric jet including a jet-parallel transition zone between warm and cold air (case II); and a circular low pressure circulation pattern with two fronts (case III).The paper presents these 3-d fields with the advantage that the analytical method is not affected by any kind of limited numerical resolution. It also shows how these fields degenerate with decreasing resolution if the analytical data are used in descrete form. This simulates working with discrete numerical data and demonstrates how narrow frontal zones of structure elements ofQ and _H ·Q considerably smooth out with increasing grid distances.With 17 Figures     

Evaluation of Haney-Type Surface ThermalBoundary Conditions Using a CoupledAtmosphere and Ocean Model

A coupled atmosphere-ocean model developed at the Institute for Space Studies at NASA Goddard Space Flight Center (Russell et al., 1995) was used to verify the validity of Haney-type surface thermal boundary condition, which linearly connects net downward surface heat flux Q to air / sea temperature difference △T by a relaxation coefficient k. The model was initiated from the National Centers for Environmental Prediction (NCEP) atmospheric observations for 1 December 1977, and from the National Ocean Data Center (NODC) global climatological mean December temperature and salinity fields at 1° ×1° resolution. The time step is 7.5 minutes. We integrated the model for 450 days and obtained a complete model-generated global data set of daily mean downward net surface flux Q, surface air temperature TA,and sea surface temperature To. Then, we calculated the cross-correlation coefficients (CCC) between Q and △T. The ensemble mean CCC fields show (a) no correlation between Q and △T in the equatorial regions, and (b) evident correlation (CCC≥ 0.7) between Q and △T in the middle and high latitudes.Additionally, we did the variance analysis and found that when k= 120 W m-2K-1, the two standard deviations, σQ and σk△T, are quite close in the middle and high latitudes. These results agree quite well with a previous research (Chu et al., 1998) on analyzing the NCEP re-analyzed surface data, except that a smaller value of k (80 W m-2K-1) was found in the previous study.