A comparison of the radar ray path equations and approximations for use in radar data assimilation

The radar ray path equations are used to determine the physical location of each radar measurement. These equations are necessary for mapping radar data to computational grids for diagnosis, display and numerical weather prediction (NWP). They are also used to determine the forward operators for assimilation of radar data into forecast models. In this paper, a stepwise ray tracing method is developed. The influence of the atmospheric refractive index on the ray path equations at different locations related to an intense cold front is examined against the ray path derived from the new tracing method. It is shown that the radar ray path is not very sensitive to sharp vertical gradients of refractive index caused by the strong temperature inversion and large moisture gradient in this case. In the paper, the errors caused by using the simplified straight ray path equations are also examined. It is found that there will be significant errors in the physical location of radar measurements if the earth’s curvature is not considered, especially at lower elevation angles. A reduced form of the equation for beam height calculation is derived using Taylor series expansion. It is computationally more efficient and also avoids the need to use double precision variables to mitigate the small difference between two large terms in the original form. The accuracy of this reduced form is found to be sufficient for modeling use.     

Variation of Radio Refractivity with Respect to Moisture and Temperature and Influence on Radar Ray Path

In this study, the variation of radio refractivity with respect to temperature and moisture is analyzed. Also, the effects of vertical gradients in temperature and moisture on the propagation paths of electromagnetic waves of weather radar are examined for several sites across the United States using several years of sounding data from the National Weather Service. The ray path is important for identifying storm characteristics and for properly using the radar data in initializing numerical weather prediction models. It is found that during the warm season the radio refractivity gradient is more sensitive to moisture gradients than to temperature gradients. Ray paths from the commonly accepted vertical ray path model are compared to a ray path computed from a stepwise ray tracing algorithm using data from actual soundings. For the sample of about 16 000 soundings examined, we find that only a small fraction of the ray paths diverge significantly from those calculated using a ray path model based on the US Standard Atmosphere. While the problem of ray dueting in the presence of a temperature inversion is fairly well known, we identify the presence of a strong vertical moisture gradient as the culprit in the majority of the cases where significant deviations occurred.     

Diurnal Variations of Thermal Roughness Height over a Grassland

The thermal roughness height associated with the surface radiation temperature has been previously found to vary between different surface types. This study finds that the thermal roughness height varies diurnally even over a homogeneous senescent grassland. The corresponding roughness length for momentum is relatively constant.Both the aerodynamic temperature and the surface radiation temperature are found to be closely related to the air temperature in the middle of the grass canopy. However, the aerodynamic temperature is strongly influenced by the horizontally integrated heat transfer, while the surface radiation temperature represents the integrated thermal emission through the grass depth within the field of view of the radiometer. The aerodynamic temperature is less sensitive to variations and measurement errors in sensible heat flux, wind speed, and air temperature than the thermal roughness height. We find that formulating the aerodynamic temperature in terms of the surface radiation temperature is better posed for use in the bulk formula than using the surface radiation temperature directly and adjusting the thermal roughness length.     

Approximate analytical solution of the nonlinear problem of a flow over a thermally inhomogeneous underlying surface

Summary The problem of the thermal circulation over the underlying surface, has been studied analytically for the case when the temperature of the underlying surface depends linearly on one of the horizontal coordinates. A horizontal pressure gradient is specified at the upper boundary of the medium horizontal layer (that has been rotating around the vertical axis) being under consideration, and this fact provides the existence of the background horizontal flow. The problem is essentially nonlinear, since, first, the heat advection, second, the square friction and the heat exchange at the underlying surface are taken into account. The solution depends on three non-dimensional parameters that are determined by the absolute values of the specified horizontal temperature and pressure gradients and by the angle between these vectors. In dependence on the values of the above mentioned parameters the solution properties may be very different. When the horizontal temperature gradient is absent, the solution is a generalization of the Ekman boundary layer classical theory for a case of the nonlinear friction against the underlying surface. The temperature and pressure fields essentially depend on the existence or absence of the background motion velocity component in the direction of the temperature horizontal gradient.With 2 Figures     

Monitoring the Sensible Heat Flux over Urban Areas using Large Aperture Scintillometry: Case Study of Marseille City During the Escompte Experiment

Abtract Sensible heat flux estimated by Large Aperture Scintillometry (LAS) has been tested against the more traditional eddy covariance technique over Marseille city centre, a reasonably homogeneous surface. Over the 3 week test period fluxes were found to be similar, yet less noisy for the LAS due to the spatial integration. No systematic bias between the estimates was found as a function of wind direction, indicating the homogeneity of the site. Sensitivity analysis of the required aerodynamic parameters shows that careful attention must be paid to the displacement height along the measurement path. Spatial variability of surface sensible heat flux is studied via a second LAS measurement path over the city.     

不同下垫面大孔径闪烁仪观测数据处理与分析

大孔径闪烁仪是近年兴起的测量大尺度（500 m~10 km）地表通量的仪器。北京师范大学等单位分别于2002年、2004年在北京昌平小汤山开展了大孔径闪烁仪短期观测实验, 2006年6月又在北京密云建立了长期观测站。利用这些数据, 对大孔径闪烁仪观测数据进行处理与分析, 结果表明:闪烁仪光径高度和风速是影响观测显热通量的关键因子。当地表粗糙元的高度变化相对于光径高度不可忽略时, 零平面位移需要精确确定。波文比在湿润地表需要准确确定, 而气温、气压和动力学粗糙度则为不敏感因子。计算中所需的大气稳定度可用理查孙数判断, 也可借助日出日落时间或净辐射观测值确定。稳定条件下的普适函数目前无统一表达式, 可采用仪器说明书推荐的函数。通过几个站点闪烁仪观测显热通量与涡动相关仪测量值的比较表明:大孔径闪烁仪在均匀和非均匀地表都能得到合理的显热通量观测值。     

Increased heat fluxes near a forest edge

Summary ?Observations of sensible and latent heat flux above forest downwind of a forest edge show these fluxes to be larger than the available energy over the forest. The enhancement averages to 56 W m⁻², or 16% of the net radiation, at fetches less than 400 m, equivalent to fetch to height ratios less than 15. The enhancement of turbulent energy fluxes is explained by advection and increases with the difference in temperature and humidity of the air over the upwind area as compared to the forest. The relatively high temperature and humidity of the upwind air are not caused by high surface heat fluxes, but are explained by the relatively low aerodynamic roughness of the upwind surface. Although the heat fluxes over forest are enhanced, the momentum fluxes are almost adjusted to the underlying forest. The different behaviour of heat and momentum fluxes is explained by absorption of momentum by pressure gradients near the forest edge. It is concluded that fetch requirements to obtain accurate surface fluxes from atmospheric observations need to be more stringent for scalar fluxes as compared to momentum fluxes. Received November 23, 2001; accepted May 13, 2002     

冬季黑潮延伸体海区海洋锋强度变化及其与北太平洋风暴轴的关系

利用英国哈德莱中心（Hadley Center）1949~2014年表层海温资料,将黑潮延伸体海区海温经向梯度的大值区域的平均值定义为黑潮延伸体及其北部海洋锋强度指数（KEFI）,利用数据分析方法研究了各季节KEFI的变化特征及其与北太平洋风暴轴的关系。分析表明,各季节的KEFI存在明显的年际和年代际变化特征,同时在冬季与北太平洋瞬时方差有显著正相关,两者在风暴轴主体位置的相关性最为显著,并且这种相关性在KEFI超前一个月时就所显现,同时对后期风暴轴也有一定影响,即冬季黑潮延伸体海区海洋锋的强度会影响风暴轴区域瞬时方差的变化。之后主要分析了这种影响的可能机制,发现在冬季KEFI高值年,由于海洋锋两侧的热量输送差异更加明显,导致海洋锋附近的近表面气温经向梯度增强,维持了近表面的斜压性,促进涡动热量的向极输送和海洋锋南侧的向上输送,有利于瞬时涡旋的发展。另外大尺度环流场与冬季黑潮延伸体海洋锋也有关系,具体表现为,在海洋锋强年,阿留申低压加深,副热带高压略有加强,对应的对流层低层位势高度场在40°N以北有负变高,以南有正变高,同时高空极锋急流加强,副热带西风急流减弱加宽北抬,海洋锋偏弱年的变化则相反。因此,冬季黑潮延伸体及其北部的海洋锋主要通过两侧海表热量输送差异不断产生气温梯度,进而维持斜压性以促进上层风暴轴的发展。     

Evaluation of Mixing-Height Retrievals from Automatic Profiling Lidars and Ceilometers in View of Future Integrated Networks in Europe

The determination of the depth of daytime and nighttime mixing layers must be known very accurately to relate boundary-layer concentrations of gases or particles to upstream fluxes. The mixing-height is parametrized in numerical weather prediction models, so improving the determination of the mixing height will improve the quality of the estimated gas and particle budgets. Datasets of mixing-height diurnal cycles with high temporal and spatial resolutions are sought by various end users. Lidars and ceilometers provide vertical profiles of backscatter from aerosol particles. As aerosols are predominantly concentrated in the mixing layer, lidar backscatter profiles can be used to trace the depth of the mixing layer. Large numbers of automatic profiling lidars and ceilometers are deployed by meteorological services and other agencies in several European countries providing systems to monitor the mixing height on temporal and spatial scales of unprecedented density. We investigate limitations and capabilities of existing mixing height retrieval algorithms by applying five different retrieval techniques to three different lidars and ceilometers deployed during two 1-month campaigns. We studied three important steps in the mixing height retrieval process, namely the lidar/ceilometer pre-processing to reach sufficient signal-to-noise ratio, gradient detection techniques to find the significant aerosol gradients, and finally quality control and layer attribution to identify the actual mixing height from multiple possible layer detections. We found that layer attribution is by far the most uncertain step. We tested different gradient detection techniques, and found no evidence that the first derivative, wavelet transform, and two-dimensional derivative techniques have different skills to detect one or multiple significant aerosol gradients from lidar and ceilometer attenuated backscatter. However, our study shows that, when mixing height retrievals from a ultraviolet lidar and a near-infrared ceilometer agreed, they were 25?C40% more likely to agree with an independent radiosonde mixing height retrieval than when each lidar or ceilometer was used alone. Furthermore, we point to directions that may assist the layer attribution step, for instance using commonly available surface measurements of radiation and temperature to derive surface sensible heat fluxes as a proxy for the intensity of convective mixing. It is a worthwhile effort to pursue such studies so that within a few years automatic profiling lidar and ceilometer networks can be utilized efficiently to monitor mixing heights at the European scale.     

The measurement of turbulent surface-layer fluxes by use of bichromatic scintillation

Scintillation measurements with a HeNe and a CO₂ laser were used to derive turbulent fluxes of heat and momentum in the surface layer. This was achieved by the structure constant or dissipation technique, i.e., by relating the measured structure constants and inner scales of refractive index fluctuations to structure constants of temperature fluctuations and dissipation rates of turbulent kinetic energy, respectively, and then assuming Monin-Obukhov similarity.The resulting heat fluxes agree well with measurements using the eddy correlation technique but for averaging periods of 10 min, the optical data show a much smoother and physically more plausible behaviour. The optically derived friction velocities are in good agreement with estimates derived from wind velocity and surface roughness. It was also observed that for stationary conditions, 1-min averaged optical measurements already provide good estimates for longer averaged heat and momentum fluxes.Even though some uncertainty remains about the empirical constants and Monin-Obukhov similarity expressions used, the method clearly proves to be of great value for monitoring surface-layer turbulence.     

Reduced Horizontal Sea Surface Temperature Gradients Under Conditions of Clear Skies and Weak Winds

Consideration of the dependence of various components of the sea-surface heat and momentum fluxes on sea surface temperature (SST) leads to an explanation for the observed reduction in the horizontal temperature gradients in the uppermost layer of the ocean (a few to 10 m in depth). Horizontal temperature gradients within the mixed layer can be masked by a near-surface layer of warm water. This camouflage of horizontal temperature gradients has importance for the remote sensing of SST used by the fishing industry, for the estimation of acoustic transmission, and for the forecasting of hurricane development, among many uses of SST data. Diurnal warming conditions in the Straits of Florida are examined by a simulation calculation and by analysis of observations obtained on moorings deployed on the south-east Florida shelf. When there is net heating (i.e., the solar input is stronger than the combined latent, sensible and longwave radiative heat losses) the originally warmer water experiences less heating than the colder water, leading to a weakening of the horizontal SST gradients as seen by surface buoys or satellites. The warmer water also experiences more mixing and therefore less increase in temperature. The strongest effect of the diurnal heating on wind stress occurs when the SST starts out cooler than the air temperature and the atmosphere is stably stratified. Diurnal warming can then rapidly increase the SST above the air temperature because of reduced wind stress and reduced upper-ocean mixing. After that the wind stress increases as convectively driven turbulence contributes to the atmospheric exchange.     

微波波段大气折射率结构常数的仿真研究

大气折射率结构常数描述了大气湍流起伏的强弱,它表征了大气折射率随机不均匀性的剧烈程度。光波和无线电波在大气中传播时会受到大气湍流的影响而产生各种不良效应,如:光斑漂移、闪烁、相位起伏等。因此,对大气折射率结构常数的研究具有重要的意义。本文利用常规探空资料对微波波段大气折射率结构常数进行了仿真研究,结果表明:在低空,特别是大气边界层之内,大气折射率结构常数主要为湿度所贡献;在高空,大气折射率结构常数主要为温度所贡献。在微波波段,影响大气折射率结构常数最大的气象因子并不是温湿压的大小,而是它们梯度的大小,其中湿度梯度的大小对其影响最大,在实际的低空测量大气折射率结构常数时,主要考虑湿度梯度与温度梯度的影响。     

DERIVATION OF FLUXES FROM PROFILES OVER A MODERATELY HOMOGENEOUS FOREST

Measurements of fluxes and profiles of wind andtemperature are performed in the roughness layer ofa moderately homogeneous forest location. Weinvestigate to what extent vertical scalar fluxescan be derived from profile measurements. Theinfluence of inhomogeneities in the upwind terrainis investigated with footprint analysis and with aninhomogeneous surface-layer model. Four methods toestimate displacement height are suggested, amongthem is a method involving the structure parameterof the vertical wind. All methods give a decrease ofdisplacement height with increasing wind speed,while roughness length is found to increase withincreasing wind speed. For near-neutral conditionsdimensionless temperature gradients are found to besubstantially lower than the surface-layer valuesfound in the literature for homogeneous terrain with lowvegetation. Dimensionless shear however iscomparable with the surface-layer value. The heightof the roughness layer is 20 times the roughnesslength. Two schemes with locally derived surfaceparameters are tested to derive friction velocityand sensible heat flux from the profilemeasurements. These site specific schemes performsatisfactorily. A third scheme based on surface parameters chosen a priorifrom the literatureperforms significantly worse especially for low windspeed and unstable cases.     

风廓线雷达反演大气比湿廓线的初步试验

基于湍流散射理论,运用边界层风廓线雷达 (WPR) 联合RASS (Radio Acoustic Sounding System), GPS/PWV (Global Position System/Precipitable Water Vapor) 进行全遥感系统的大气比湿廓线反演试验,并对影响因子进行分析。利用2011年8—9月云南大理综合探测试验数据的反演结果与探空数据进行比较分析,结果表明:WPR联合探空的温度廓线和起始边界比湿 (q₀) 反演大气比湿廓线,与探空大气比湿廓线相比具有相同的变化趋势,标准差为0.84 g·kg-1,误差随高度增加呈递增趋势;WPR联合RASS, GPS/PWV数据反演大气比湿廓线,与探空大气比湿廓线的标准差为0.85 g·kg-1。参加反演的数据中,折射指数结构常数C_n2与谱宽σ_turb2对反演影响最大,反演算法中大气折射指数梯度M符号的判断对反演精度也有较大影响。     

Determining surface roughness and displacement height

Vertical flux densities of momentum and sensible heat, obtained from simultaneous wind speed and air temperature profiles in the surface layer, depend on the displacement height of the profile system and the surface roughness. A criterion for selecting the displacement height and the surface roughness is introduced, which requires a minimum value for the error squares between the observed and a calculated wind speed profile as determined by diabatic surface layer theory. Values of displacement height and surface roughness, which provide a minimum error squares fit within a desired tolerance, are selected by the rule of false position. The method is programmed for digital computer solution and applied to a total number of 628 profiles obtained during a 7-day period at a micrometeorological test site near Davis, California, using five measurement levels to 160 cm height.     

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.     

温江站夏季大气边界层垂直结构特征

利用温江观测站边界层塔和探空获取的观测资料,从地表物理量的日变化、边界层的垂直结构及逐日变化这些方面分析该站夏季边界层特征,得到以下结论:(1)地表各物理量都具有明显的日变化特征,呈现一峰一谷的演变状态,其中地表热通量、动量通量、气温以及风速的峰值皆出现在午后,谷值出现在凌晨,湿度与气温日变化是反位相的。(2)近地层低层大气气温在早晚时段,随高度的增加而上升,呈逆温状态;午间时段随高度的增加而下降。9 m以下大气在午后的比湿梯度最大。风速值随着高度的增高而增大,风切变随着高度的增高而减小。(3)探空观测的边界层垂直结构显示:夏季温江站早晚边界层大气层结稳定,而午后表现为典型的混合边界层特征。大气温/湿度差异随高度增长而降低,各个时次温/湿度的差异都主要集中边界层低层,越靠近地面大气温/湿度差异越突出。8:00的温度最低,14:00最高。14:00的大气比湿最小,2:00和20:00较大。近地层风速随高度增长较快,在离地2~300 m左右高度达到一个极值,4个时次的风速差异不大。(4)地表温度、短波辐射、感热通量对边界层的高度和降水都有一定的影响。     

Influence of Source/Sink Distributions on Flux–Gradient Relationships in the Roughness Sublayer Over an Open Forest Canopy Under Unstable Conditions

The flux–gradient relationships in the unstable roughness sublayer (RSL) over an open canopy of black spruce forest were examined using long-term observations from an instrumented tower. The observed gradients normalised with the surface fluxes and height above the zero-plane displacement showed differences from a universal function established in the surface layer. The magnitude of differences was not constant throughout the year even at the same observation height. Also the magnitude of the differences was different for each scalar, and scalar similarity in the context of the flux–gradient relationship did not always hold. The variation of the differences was explained by the relative contribution of overstorey vegetation to the total flux from the entire ecosystem. This suggests that a mismatch of the vertical source/sink distributions between scalars leads to a different strength of the near-field dispersion effect for each scalar, and this resulted in inequality of eddy diffusivity among scalars in the RSL. An empirical method that predicts the magnitude of differences is proposed. With this method, it is possible to estimate the eddy diffusivity of scalars provided that the relative contribution of overstorey vegetation to the total flux from the ecosystem is known. Also this method can be used to estimate the eddy diffusivity for scalars whose primary sources are at ground level, such as methane and nitrous oxide.