计算非均一大气条件下太阳辐射通量的一个简单而又精确的模式

发展了一个计算非均一大气条件下太阳辐射通量的一个简单而又精确的模式，其中包括关于大气球反射率与透过率的一个参数化表达式，并引入加权一次散射反照率和加权不对称因子，用于拟合非均一大气条件下计算辐射通量的四个经验订正因子。对清洁和浑浊的两类大气，都具有120060组的辐射通量模拟试验，以检验本模式的精度。这些模拟试验覆盖0－50的云光学厚度、0－0．8地表反射率、Junge和对数正态的气溶胶谱分布、－0．05气溶胶折射率虚部。在均一大气条件下，由本模式计算的120060组向上通量的标准差对清洁和浑浊两类大气分别为1．08％和1．04％；而向下通量的标准差分别为4.12%和3．31％。在非均一大气条件下，由本模式计算的向上通量的标准差对清洁和浑浊两类大气分别为3．01％和3．48％；而向下通量的标准差分别为4．54％和4．89％，其精度远优于均一假设下的计算结果。     

大气气溶胶的垂直非均一对向上亮度和卫星遥感地表反射率的效应

均一模式和两层模式是两个忽略气溶胶垂直非均一、并广泛用于卫星遥感的辐射模式。通过两个模式的数值模拟，分析了气溶胶的垂直非均一对向上天空亮度和卫星遥感地面反射率的效应。数值模拟选用了２４个有代表性的气溶胶模式。对于具有强分子散射的卫星短波通道，由于分子和气溶胶散射性的明显不同，应用均一和两层模式计算的向上亮度往往存在较大误差。对长波通道，如果气溶胶的光学特性随高度变化不大，该亮度误差较小，但如果存在不同散射相函数和一次散射反照率的气溶胶层，该误差仍可能较大。对于干净的大气，由均一和两层模式计算的亮度误差可分别高达３１．４％和３１．５％，而对于混浊的大气，该误差可分别高达６７．８％和５９．２％。该亮度误差可以引起地表反射率解存在大的不确定性，特别是对于短波通道和强吸收的气溶胶。对于包含强吸收气溶胶的混浊大气，均一和两层模式不适合于大气订正应用。     

Aircraft observations of solar radiation in cloud-free atmospheres

Aircraft observations of solar radiative fluxes (including the downward diffuse component) made in cloud-free conditions in the lowest 8 km of the atmosphere, have been interpreted using simultaneous measurements of aerosol characteristics. Measured flux profiles have been compared with those derived from a two-stream model of radiative transfer which can incorporate both gaseous and aerosol effects. In one of the four cases examined, sufficient aerosol data were available to estimate the radiative properties of the aerosol which could then be included in the model calculations. The findings are shown to be broadly consistent with the observations when a realistic aerosol refractive index is used. The measurement of the downward diffuse radiation enabled the radiative properties of the aerosol to be calculated directly from the flux measurements. In particular, the average single-scattering albedo of aerosol within the boundary layer in continental air masses was estimated to be about 0.7.The implications of having a highly absorbing aerosol present within the boundary layer are also considered. In one case a heating rate of about 5 K day^-1 was observed across the aerosol layer, which suggests that on occasions, aerosol heating will be a significant term in the heat budget for the boundary layer.     

Cloud-Aerosol-Radiation (CAR) ensemble modeling system: Overall accuracy and efficiency

The Cloud-Aerosol-Radiation (CAR) ensemble modeling system has recently been built to better understand cloud/aerosol/radiation processes and determine the uncertainties caused by different treatments of cloud/aerosol/radiation in climate models. The CAR system comprises a large scheme collection of cloud, aerosol, and radiation processes available in the literature, including those commonly used by the world's leading GCMs. In this study, detailed analyses of the overall accuracy and efficiency of the CAR system were performed. Despite the different observations used, the overall accuracies of the CAR ensemble means were found to be very good for both shortwave (SW) and longwave (LW) radiation calculations. Taking the percentage errors for July 2004 compared to ISCCP (International Satellite Cloud Climatology Project) data over (60°N, 60°S) as an example, even among the 448 CAR members selected here, those errors of the CAR ensemble means were only about-0.67% (-0.6 W m-2 ) and-0.82% (-2.0 W m-2 ) for SW and LW upward fluxes at the top of atmosphere, and 0.06% (0.1 W m-2 ) and -2.12% (-7.8 W m-2 ) for SW and LW downward fluxes at the surface, respectively. Furthermore, model SW frequency distributions in July 2004 covered the observational ranges entirely, with ensemble means located in the middle of the ranges. Moreover, it was found that the accuracy of radiative transfer calculations can be significantly enhanced by using certain combinations of cloud schemes for the cloud cover fraction, particle effective size, water path, and optical properties, along with better explicit treatments for unresolved cloud structures.     

多层四流球谐函数算法的构建及在大气辐射传输模式中的应用

为了在不大幅度增加计算成本的情况下提高大气辐射传输计算的精度,利用单层四流球谐函数结合多层二流累加法,构造了可用于多层大气的四流球谐函数算法。为了比较与其他辐射传输算法的差异,引入48流离散纵坐标算法作为比较标准,Eddington 近似、四流离散纵坐标算法作为比较对象。在真实大气廓线条件下,计算了晴空和有云大气顶向上辐射通量、地表向下辐射通量以及加热率廓线。得出以下结论：在晴空情况下,与作为标准的48流离散纵坐标法相比,Eddington 近似、四流离散纵坐标法和新构造的四流球谐函数方法加热率绝对误差都小于0?3 K／d;向上、向下辐射通量的相对误差分别小于1％和0?6％。这表明在晴空情况下,3种算法对加热率的计算精度差别不大;对辐射通量的计算精度,两种四流近似算法比传统的 Eddington 近似更为精确。在有云情况下,与48流离散纵坐标法相比,四流球谐函数和四流离散纵坐标法计算的云顶加热率相对误差小于1％,而 Eddington 近似计算的云顶加热率相对误差大于5％。结果表明：新构造的四流球谐函数算法可用于大气辐射传输模式,在不大幅度增加计算成本的同时,提高了晴空大气的整体辐射计算精度和有云大气辐射加热率的计算精度。     

中国地区夏季平均加热率的时空分布特征

The latitude-altitude distributions of radiative fluxes and heating rates are investigated by utilizing CloudSat satellite data over China during summer. The Tibetan Plateau causes the downward shortwave fluxes of the lower atmosphere over central China to be smaller than the fluxes over southern and northern China by generating more clouds. The existence of a larger quantity of clouds over central China reflects a greater amount of solar radiation back into space. The vertical gradients of upward shortwave radiative fluxes in the atmosphere below 8 km are greater than those above 8 km. The latitudinal-altitude distributions of downward longwave radiative fluxes show a slantwise decreasing trend from low latitudes to high latitudes that gradually weaken in the downward direction. The upward longwave radiative fluxes also weaken in the upward direction but with larger gradients. The maximum heating rates by solar radiation and cooling rates by longwave infrared radiation are located over 28-40°N at 7-8 km mean sea level (MSL), and they are larger than the rates in the northern and southern regions. The heating and cooling rates match well both vertically and geographically.     

Optical properties of a vertically inhomogeneous mid-latitude mid-level mixed-phase altocumulus in the infrared region

A vertically inhomogeneous mid-latitude mixed-phase altocumulus cloud was observed around 17:26 UTC on Oct. 14, 2001 during the 9th Cloud Layer Experiment (CLEX9). In this study the microphysical and optical properties of this cloud are investigated on the basis of in-situ observed vertical profiles of particle size and habit distributions. Two cloud models, assuming that the cloud properties were vertically homogeneous and inhomogeneous, are adopted to derive the bulk optical and radiative properties of this cloud. The observed microphysical properties are combined with the theoretical solutions to the scattering and absorption properties of individual cloud particles to determine the bulk optical properties at various heights within the cloud layer. The single-scattering properties of spherical liquid water droplets and nonspherical ice crystals are obtained from the Lorenz–Mie theory and an existing database, respectively. The bulk microphysical and optical properties associated with the inhomogeneous model depend strongly on the height above the cloud-base whereas the dependence is smoothed out in the case of the homogeneous model. Furthermore, the transfer of infrared radiation is simulated in conjunction with the two cloud models. It is shown that the brightness temperatures at the top of the atmosphere in the case of the homogeneous model can be 1.5% (3.8 K) higher than their counterpart associated with the inhomogeneous cloud model. This result demonstrates that the effect of the vertical inhomogeneity of a mixed-phase cloud on its radiative properties is not negligible.     

Impact of Different Aerosols on the Evolution of the Atmospheric Boundary Layer

The present work analyzes the effect of aerosols on the evolution of the atmospheric boundary layer (ABL) over Shangdianzi in Beijing.A one-dimensional ABL model and a radiative transfer scheme are incorporated to develop the structure of the ABL.The diurnal variation of the atmospheric radiative budget,atmospheric heating rate,sensible and latent heat fluxes,surface and the 2 m air temperatures as well as the ABL height,and its perturbations due to the aerosols with different single-scattering albedo (SSA) are studied by comparing the aerosol-laden atmosphere to the clean atmosphere.The results show that the absorbing aerosols cause less reduction in surface evaporation relative to that by scatting aerosols,and both surface temperature and 2 m temperature decrease from the clean atmosphere to the aerosol-laden atmosphere.The greater the aerosol absorption,the more stable the surface layer.After 12:00 am,the 2 m temperature increases for strong absorption aerosols.In the meantime,there is a slight decrease in the 2 m temperature for purely scattering aerosols due to radiative cooling.The purely scattering aerosols decrease the ABL temperature and enhance the capping inversion,further reducing the ABL height.     

Influences of Physical Processes and Parameters on Simulations of TOA Radiance at UV Wavelengths: Implications for Satellite UV Instrument Validation

Numerous factors can influence the radiative transfer simulation of hyper-spectral ultraviolet satellite observation,including the radiative transfer scheme, gaseous absorption coefficients, Rayleigh scattering scheme, surface reflectance, aerosol scattering, band center wavelength shifts of sensor, and accuracy of input profiles. In this study, a Unified Linearized Vector Radiative Transfer Model(UNL-VRTM) is used to understand the influences of various factors on the top of atmosphere(TOA) normalized radiance in the ultraviolet(UV) region. A benchmark test for Rayleigh scattering is first performed to verify the UNL-VRTM accuracy, showing that the model performances agree well with earlier peer-reviewed results. Sensitivity experiments show that a scalar radiative transfer approximation considering only ozone and a constant surface reflectance within the UV region may cause significant errors to the TOA normalized radiance. A comparison of the Ozone Mapping and Profiler Suite(OMPS) radiances between simulations and observations shows that the surface reflectance strongly influences the accuracy for the wavelengths larger than 340 nm. Thus, using the surface reflectivity at 331 nm as a proxy for simulating the whole OMPS hyperspectral ultraviolet radiances is problematic. The impact of rotational Raman scattering on TOA radiance can be simulated through using SCIATRAN, which can also reduce the difference between measurements and simulations to some extent. Overall, the differences between OMPS simulations and observations can be less than 3% for the entire wavelengths. The bias is nearly constant across the cross-track direction.     

Time and height variability of the sensible heat flux in the surface layer

The energy-budget concept is used together with a high resolution spectral radiation model to study the time and height variation of the sensible heat flux and of the eddy thermal diffusivity for an actual case up to 50 m above ground. A data set of 32 h is chosen for this study. Time-height cross-sections of the local enthalpy changes, and the radiative and the sensible heat flux divergences are presented, which show the interaction of the two energy fluxes. It can be seen, for example, that during the transient hours from night to day the sensible heat flux divergence plays an outstanding role in the warming of the atmosphere, while during the clear night radiative cooling exceeds the cooling caused by the sensible heat flux. For the layer under consideration (0-50 m) a constancy of the sensible heat flux within 10% is obtained for seven hours only, namely for the time around noon and in the early afternoon. Selected night-time profiles of the thermal diffusivity are shown, which have their maximum below 48.3 m.The accuracy of the energy-budget method is studied in detail. The tests show that a high accuracy, with errors even less than 10% for some hours, can be expected, if special micrometeorological studies are made during the field phase and a layer depth of 50 cm or less is used in the radiation model.     

INFLUENCE OF CLOUDS ON TRANSMITTED SOLAR RADIATION ABOVE AN INHOMOGENEOUS GROUND SURFACE

Monte-Carlo method has been applied to investigate the radiance and radiative flux on the horizontallyinhomogeneous ground surface in a cloudy atmosphere.It has been found that the characteristics of theground radiance and flux are significantly changed by clouds.The flux in the quadrant toward the surfacewith higher reflectivity are greater than that toward the surface with lower reflectivity.And the flux variesacross the boundary of the two areas with different surface albedos.The effect of inhomogeneity of the surfacealbedo in a cloudy atmosphere can extend far to 20 km.In addition,the horizontal distribution of the fluxabsorbed by the ground is more homogeneous in a cloudy atmosphere than that in a clear air.     

北京一次污染过程气溶胶光学特性及辐射效应

利用地面激光雷达、太阳光度计观测反演气溶胶光学特性参数,结合PM_2.5观测数据,分析了2018年1月25—28日北京一次完整污染过程中气溶胶光学特性变化。基于观测数据,利用短波辐射传输模式计算了不同程度污染日,晴空背景下气溶胶对辐射加热率的改变程度。结果表明:清洁日（25日）,PM_2.5日平均质量浓度为19.00 μg·m-3,440 nm气溶胶光学厚度为0.13,单次散射反照率为0.87,整层气溶胶消光系数低于0.10 km-1,短波辐射均为增温效应;污染期间（26—27日）,PM_2.5日平均质量浓度为83.21 μg·m-3,气溶胶光学厚度为2.48,气溶胶散射能力增强,单次散射反照率达到0.94,气溶胶主要消光层厚度提升至3.00 km高度,消光系数平均值为0.43 km-1,气溶胶在垂直方向的变化导致气溶胶中上层（1.50~3.00 km高度）加热作用强烈,短波辐射加热率平均值达到13.89 K·d-1,而低层（1.50 km高度以内）加热作用较弱,加热率平均值仅为0.99 K·d-1。气溶胶散射能力增强导致加热作用减弱,污染日加热率对于气溶胶散射能力变化更敏感。     

NASA/Goddard长波辐射方案在GRAPES_Meso模式中的应用研究

本文将NASA（National Aeronautics and Space Administration）/Goddard长波辐射方案引入到GRAPES_ Meso（Global/Regional Assimilation and PrEdiction System_Meso）模式中,对2006年4月中国地区进行了一个月的模拟试验,并与相应的NCEP（National Centers for Environmental Prediction）再分析资料进行了对比分析。试验结果表明:在模拟区域内,使用GRAPES_Meso模式进行24 h、48 h预报得到的晴空大气顶向外长波辐射通量（the clear sky outgoing longwave radiation flux,OLRC）、地面接收到向下长波辐射通量（the clear sky downward longwave radiation flux at ground,GLWC）分布形势与NCEP再分析资料具有较好的对应关系;模式预报24 h、48 h OLRC和NCEP再分析资料月平均误差百分比控制在－10%～＋10%以内,GLWC月平均误差百分比比OLRC略大,但总体上两者误差都在合理和可接受范围之内。OLRC和GLWC 24 h、48 h的预报和NCEP再分析资料的逐日距平相关系数及标准误差的对比显示,模式24 h预报OLRC、GLWC的距平相关系数月平均值分别为0.96、0.98,标准误差月平均值分别为24.54 W m-2、27.23 W m-2;模式48 h预报OLRC、GLWC的距平相关系数月平均值分别为0.9521、0.9804,标准误差月平均值分别为22.43 W m-2、27.64 W m-2。总体上,模式24 h、48 h预报OLRC和GLWC的距平相关系数都在0.93以上,标准误差都在31 W m-2以内,且GLWC预报和NCEP再分析资料的相关性比OLRC略好,OLRC预报与NCEP再分析资料的的标准误差比GLWC略小。通过和RRTM长波辐射方案对比可知,两者的预报水平基本一致。本文研究结果表明,引入NASA/Goddard长波辐射方案后的GRAPES_Meso模式整体上能够较好地预报OLRC和GLWC,该辐射方案可以作为模式GRAPES_Meso的备选辐射方案之一。     

Thermal radiative fluxes through inhomogeneous cloud fields: a sensitivity study using a new stochastic cloud generator

We analyze the effects of flat and bumpy top, fractional and internally inhomogeneous cloud layers on large area-averaged thermal radiative fluxes. Inhomogeneous clouds are generated by a new stochastic model: the tree-driven mass accumulation process (tdMAP). This model is able to provide stratocumulus and cumulus cloud fields with properties close to those observed in real clouds. A sensitivity study of cloud parameters is done by analyzing differences between 3D fluxes simulated by the spherical harmonic discrete ordinate method and three “standard” models likely to be used in general circulation models: plane-parallel homogeneous cloud model (PPH), PPH with fractional cloud coverage model (FCPPH) and independent pixel approximation model (IPA). We show that thermal fluxes are strong functions of fractional cloud coverage, mean optical depth, mean geometrical thickness and cloud base altitude. Fluctuations of “in-cloud” horizontal variability in optical depth and cloud-top bumps have negligible effects in the whole. We also showed that PPH, FCPPH and IPA models are not suitable to compute thermal fluxes of flat top fractional inhomogeneous cloud layer, except for completely overcast cloud. This implies that horizontal transport of photon at thermal wavelengths is important when cloudy cells are separated by optically thin regions.     

基于FY-3/IRAS利用非线性模式反演OLR

FY-3系列卫星星载IRAS仪器设有26个通道,其中20个通道用于探测地球大气在红外波段的热辐射,通道辐射率代表了地球大气系统在大气顶的向外辐射光谱信息,与总波段的射出长波辐射（OLR）通量相关性高。该文基于逐线辐射传输模式计算软件LBLRTM对全球2521条大气廓线的大气顶射出辐射率模拟数据,计算了每条廓线的OLR和FY-3B/IRAS,FY-3C/IRAS通道辐射率,用统计回归方法建立了利用IRAS的多通道辐射率计算OLR的非线性理论回归模式;应用模式和FY-3B/IRAS,FY-3C/IRAS的L1级数据,处理得到2016年4月1-30日的全球日平均、月平均OLR格点产品。与Aqua/CERES,Terra/CERES仪器宽波段观测OLR产品对比表明:对于水平分辨率为1°×1°的全球月平均OLR格点产品,均方根误差为2.22 W·m-2,相关系数为0.9982 W·m-2,平均偏差为-0.2 W·m-2,表明FY-3/IRAS仪器定标及反演模式均达到较高水平。文中还回顾了历史上不同气象卫星的多种OLR反演算法模式,并对不同模式精度进行了比较。     

Direct Radiative Forcing of Anthropogenic Aerosols over Oceans from Satellite Observations

Anthropogenic aerosols play an important role in the atmospheric energy balance. Anthropogenic aerosol optical depth (AOD) and its accompanying shortwave radiative forcing (RF) are usually simulated by nu- merical models. Recently, with the development of space-borne instruments and sophisticated retrieval algorithms, it has become possible to estimate aerosol radiative forcing based on satellite observations. In this study, we have estimated shortwave direct radiative forcing due to anthropogenic aerosols over oceans in all-sky conditions by combining clouds and the Single Scanner Footprint data of the Clouds and Earth’s Radiant Energy System (CERES/SSF) experiment, which provide measurements of upward shortwave fluxes at the top of atmosphere, with Moderate Resolution Imaging Spectroradiometer (MODIS) aerosol and cloud products. We found that globally averaged aerosol radiative forcing over oceans in the clear-sky conditions and all-sky conditions were -1.03±0.48 W m-2 and -0.34 ±0.16 W m-2, respectively. Direct radiative forcing by anthropogenic aerosols shows large regional and seasonal variations. In some regions and in particular seasons, the magnitude of direct forcing by anthropogenic aerosols can be comparable to the forcing of greenhouse gases. However, it shows that aerosols caused the cooling effect, rather than warming effect from global scale, which is different from greenhouse gases.     

Radiative effects of Pinatubo aerosols in the middle latitudes of the Northern Hemisphere

Summary Using scattering coefficient profiles of the Pinatubo aerosols derived from the observation of skylight polarization and lidar backscattering ratio in Beijing, the radiative effect of Pinatubo aerosols in middle latitudes is assessed by a delta-four-stream radiative transfer model. It is shown that the Pinatubo aerosols significantly change the radiation field. Due to the presence of the volcanic aerosols, the downward short wave flux at the surface decreases with a maximum of 8 W/m² while the upward short wave flux at the top of the atmosphere increases with a maximum of 6.5 W/m². The volcanic aerosols are injected into the region bounded below by the tropopause and up by the 25 km level. The upward and downward radiative fluxes are changed in opposite directions at those two boundaries. Downward short wave fluxes below the tropopause are 7–9 W/m² less than background values and downward long wave fluxes below the tropopause are 2 W/m² more than background values. Upward short wave fluxes above 25 km level is 5–7 W/m² more and upward fluxes above there are about 3 W/m² less.The effects of the Pinatubo aerosols on heating rates are also significant. The maximum increase in the short wave heating rate can be as large as 0.2 K/day at 22 km. The increase in the long wave heating rate is less with a maximum amplitude of about 0.15 K/day. The maximum increase of the total heating rate is about 0.35 K/day, which is comparable with the heating rate caused by the ozone 9.6 µm band in this region.Results of this study are compared with studies of Lacis et al. (1992) and Russell et al. (1993) as well as ERBE measurements. The results generally agree well. Causes for the differences are analyzed.Based on the numerical study, it is also found that the LOWTRAN fresh volcanic model is not representative for the Pinatubo aerosols.With 9 Figures     

从Himawari08卫星估算晴空地表长波辐射及其日变化特征初探

通过446183条全球晴空大气廓线的红外辐射传输模拟和统计回归,建立了由Himawari08成像仪通道遥测数据估算晴空地表上行、下行长波辐射通量的反演模式,模式应用于成像仪观测资料,处理出晴空地表上行、下行长波辐射通量实时产品,2016年2~6月的产品精度验证试验结果为:与相同时刻的AQUA卫星CERES仪器同类产品相比,地表上行通量均方根误差R_e=7.9 W/m2,相关系数R=0.9399,地表下行通量R_e=14.5 W/m2,R=0.9586;与由中国地面气象站地面气温和相对湿度观测经Brunt、Brutsaert经验公式计算的实时地表下行长波辐射通量相比,R_e=15.34 W/m2,R=0.8786;与用陆表温度计算的地表上行长波辐射通量相比,R_e=12.6 W/m2,R=0.9977。研究了2016年2、6月的晴空地表长波辐射产品,发现陆地晴空上、下行通量有着与太阳加热地表增温相应的明显日变化特征,峰值出现在12:00（当地时间,下同）至14:00,低谷出现在04:00至07:00,下行通量与上行通量几乎同步变化或约有延时,陆地上2个通量归一化的日变化指数类似一个半正弦曲线,而海面长波辐射通量则没有明显的日变化规律。     

The aerosol module in the INM RAS climate model

The aerosol module is included into the INM RAS climate model. The module computes the evolution of main aerosols: sea salt, mineral dust, sulfate aerosol, and black and organic carbon. Aerosol surface fluxes, advection, gravitational sedimentation, surface absorption, and scavenging by precipitation are taken into account to compute aerosol concentration variations. Model aerosol distribution is used to compute radiation fluxes. The ten-year run of the climate model is performed. The climatology of model aerosol is considered. The aerosol mass, integral source values, optical thickness, and radiative forcing are presented. The results are compared with the data of other models and observations.     

Flux Footprint Simulation Downwind of a Forest Edge

Surface fluxes, originating from forest patches, are commonly calculated from atmospheric flux measurements at some height above that patch using a correction for flux arising from upwind surfaces. Footprint models have been developed to calculate such a correction. These models commonly assume homogeneous turbulence, resulting in a simulated atmospheric flux equal to the average surface flux in the footprint area. However, atmospheric scalar fluxes downwind of a forest edge have been observed to exceed surface fluxes in the footprint area. Variations in atmospheric turbulence downwind of the forest edge, as simulated with an E – model, can explain enhanced atmospheric scalar fluxes. This E – model is used to calculate the footprint of atmospheric measurements downwind of a forest edge. Atmospheric fluxes appear mainly enhanced as a result of a stronger sensitivity to fluxes from the upwind surface. A sensitivity analysis shows that the fetch over forest, necessary to reach equilibrium between atmospheric fluxes and surface fluxes, tends to be longer for scalar fluxes as compared to momentum fluxes. With increasing forest density, atmospheric fluxes deviate even more strongly from surface fluxes, but over shorter fetches. It is concluded that scalar fluxes over forests are commonly affected by inhomogeneous turbulence over large fetches downwind of an edge. It is recommended to take horizontal variations in turbulence into account when the footprint is calculated for atmospheric flux measurements downwind of a forest edge. The spatially integrated footprint is recommended to describe the ratio between the atmospheric flux and the average surface flux in the footprint.