Aerosol optical thickness retrieval over non-Lambertian land surface with synergistic use of AATSR radiance measurements and MODIS derived Albedo Model Parameters

Various algorithms have recently been developed in order to retrieve the aerosol optical thickness (AOT) at continental scales. However, they are, to some extent, subject to large uncertainties resulting from some necessary physical assumptions on land surface anisotropy and level of brightness. In fact, disentangling aerosol and surface signals contained in the top of atmosphere (TOA) radiance received at the satellite level are a matter of difficulty because a single sensor itself cannot gather all required spatial, temporal, spectral and angular information. In particular, each instrument yields limited scanning configuration due to its platform's orbital characteristics. In this regard, a synergetic approach is presented which merges Advanced Along-Track Scanning Radiometer (AATSR) TOA radiances and the MODerate resolution Imaging Spectroradiometer (MODIS) Bi-directional Reflectance Distribution Function (BRDF)/Albedo Model Parameters Product for the retrieval of AOT at 0.55, 0.66, and 0.87 µm wavelengths over non-Lambertian land surface at a 5 km spatial resolution. In this approach, BRDF products serve to assess the surface reflectance in the AATSR geometry as a boundary layer. The peculiarity of the approach is that no specific assumption is required about the spectral characteristics of land surface, thus allowing for a quantitative retrieval of aerosol particles over any arbitrary land unit in virtue of combining forward and nadir AATSR observations. We obtain on average differences within 0.1τ compared to in situ AErosol RObotic NETwork (AERONET) measurements and 36 retrievals corresponding to 27 January, 12 February, 16 March, 28 May, 26 June, and 21 July 2006, respectively, over the city of Beijing in China. Pearson's correlation coefficient is 0.94 and 0.96 for nadir and forward AATSR, respectively. These suggest that AOT retrieval over land is indeed feasible by taking benefit of the validated MODIS BRDF. Besides, the first results indicate that the AATSR retrievals might be used to evaluate the spectral behaviour of the AOT.     

Measurements of desert dust optical characteristics at Porte au Sahara during SAMUM

Main optical characteristics of desert dust, such as phase function and single scattering albedo, have been derived from combinations of sun-/sky-radiometer and satellite measurements during the SAMUM experiment (10 May–10 June 2006) at the site Porte au Sahara (30.237°N, 5.607°W) in South Morocco. Scattering phase functions have been retrieved using combined data of spectral aerosol optical thickness (AOT) and spectral sky brightness in the almucantar, considering non-spherical light scattering. Intercomparisons of modelled top-of-atmosphere (TOA) reflectance with satellite observations of the Medium Resolution Imaging Spectrometer (MERIS) and Scanning Imaging Absorption Spectrometer for Atmospheric Chartography () instrument have been used for the estimation of spectral single scattering albedo. For the radiative transfer calculations scattering phase functions and AOT from ground-based observations have been used. The spectral single scattering albedo ranges from 0.93 in the blue to 0.98 at 753 nm.     

Desert dust aerosol air mass mapping in the western Sahara, using particle properties derived from space-based multi-angle imaging

Coincident observations made over the Moroccan desert during the Sahara mineral dust experiment (SAMUM) 2006 field campaign are used both to validate aerosol amount and type retrieved from multi-angle imaging spectroradiometer (MISR) observations, and to place the suborbital aerosol measurements into the satellite's larger regional context. On three moderately dusty days during which coincident observations were made, MISR mid-visible aerosol optical thickness (AOT) agrees with field measurements point-by-point to within 0.05–0.1. This is about as well as can be expected given spatial sampling differences; the space-based observations capture AOT trends and variability over an extended region. The field data also validate MISR's ability to distinguish and to map aerosol air masses, from the combination of retrieved constraints on particle size, shape and single-scattering albedo. For the three study days, the satellite observations (1) highlight regional gradients in the mix of dust and background spherical particles, (2) identify a dust plume most likely part of a density flow and (3) show an aerosol air mass containing a higher proportion of small, spherical particles than the surroundings, that appears to be aerosol pollution transported from several thousand kilometres away.     

中国区域MODIS陆上气溶胶光学厚度产品检验

以我国MODIS共享网站积累的MODIS L1B数据和美国威斯康辛大学提供的IMAPP软件包气溶胶产品软件为基础, 经过产品运行本地化改进处理, 在国家卫星气象中心建立了气溶胶产品业务化生成和发布机制。为支持气溶胶遥感产品算法改进以及潜在用户对产品的合理应用, 给出对国家卫星气象中心运行的MODIS气溶胶遥感产品质量检验分析结果。利用2005年1月— 2007年5月AERONET地基气溶胶监测网的L2.0级气溶胶光学厚度产品作为真值, 用它匹配MODIS陆上气溶胶光学厚度产品开展检验。检验结果表明:以卫星过境前后30min地基观测时间平均值匹配地基站点位置10 km半径范围内的卫星反演结果空间平均值开展检验, 总体样本的气溶胶光学厚度均方根误差约为0.25;满足产品误差要求 (±0.05±0.20τ) 的样本占总样本数的44%; 气溶胶光学厚度反演结果精度具有季节和地域差异, 干季(秋、冬、春)的气溶胶光学厚度误差较小, 而雨季气溶胶光学厚度误差较大, 云是雨季气溶胶光学厚度反演结果误差较大的主要影响因素。     

Detection of Sahara dust intrusions during mixed advection patterns over south-east Italy: A case study

Measurements from July 4 to July 8, 2005 by a high resolution visible radiometer, a Raman lidar, a ground particulate matter sampler, and ground meteorological sensors have been combined in synergy to infer the intrusion over south-east Italy, of air masses from north-west Sahara, the Atlantic Ocean, and the continental Europe. It is shown that backscatter coefficient, depolarization-ratio, and lidar ratio vertical profiles represent the best tools to detect the intrusion of long range transported air masses and to monitor their effects on the vertical distribution of aerosol optical and microphysical properties. High resolution radiometers are instead important tools to monitor changes on columnar aerosol properties and size distributions.Backscatter coefficient, depolarization-ratio, and lidar ratio vertical profiles have revealed that aerosol optical and microphysical properties significantly changed with time and space during African dust outbreaks: the intrusion of dust particles that at first occurred above 2 km of altitude extending up to 6 km, affected the all aerosol load down to ground within few hours. Aerosol size distributions showed during dust events a clear bimodality with an accumulation mode maximum at 0.24 µm and a coarse mode maximum at 0.94 μm. Conversely, we have found that during the advection of air masses from the Atlantic and continental Europe, aerosol particles were mainly located below 2 km, their optical and microphysical properties were affected by smaller changes in time and space, and were characterized by depolarization ratios rather close to those due to a pure molecular atmosphere. In this case bimodal size distributions with an accumulation mode showing two sub-modes at 0.16 μm and 0.24 μm, respectively and a coarse mode centred at 0.94 μm have also been observed.     

Short-wave aerosol radiative efficiency over the global oceans derived from satellite data

Using 5 yr (December 2000–November 2005) of satellite data from the clouds and the earths radiant energy system (CERES) and moderate resolution imaging spectroradiometer (MODIS), we examine the instantaneous short-wave radiative efficiency ( E_τ ) of aerosols during the morning Terra satellite overpass time over the global oceans (60°N–60°S). We calculate E_τ using two commonly used methods. The first method uses the MODIS aerosol optical thickness (AOT) at 0.55 μm with radiative transfer calculations, whereas the second method utilizes the same AOT values along with a new generation of aerosol angular distribution models to convert the CERES-measured broad-band radiances to fluxes. Over the 5 yr, the global mean instantaneous E_τ between the methods is remarkably consistent and within 5 W m⁻²τ⁻¹ with a mean value of –70 W m⁻²τ⁻¹. The largest differences between the methods occur in high-latitude regions, primarily in the Southern Hemisphere, where AOT is low. In dust dominated regions, there is an excellent agreement between the methods with differences of <3 W m⁻²τ⁻¹. These differences are largely due to assumptions in aerosol models and definition of clear sky backgrounds. Independent assessments of aerosol radiative effects from different satellite sensors and methods are extremely valuable and should be used to verify numerical modelling simulations.     

Retrieval of aerosol optical properties over a vegetation surface using multi-angular,multi-spectral,and polarized data

An algorithm to retrieve aerosol optical properties using multi-angular,multi-spectral,and polarized data without a priori knowledge of the land surface was developed.In the algorithm,the surface polarized reflectance was estimated by eliminating the atmospheric scattering from measured polarized reflectance at 1640 nm.A lookup table （LUT） and an iterative method were adopted in the algorithm to retrieve the aerosol optical thickness （AOT,at 665 nm） and the （A）ngstr（o）m exponent （computed between the AOTs at 665 and 865 nm）.Experiments were performed in Tianjin to verify the algorithm.Data were provided by a newly developed airborne instrument,the Advanced Atmosphere Multi-angle Polarization Radiometer （AMPR）.The AMPR measurements over the target field agreed well with the nearby ground-based sun photometer.An algorithm based on Research Scanning Polarimeter （RSP） measurements was introduced to validate the observational measurements along a flight path over Tianjin.The retrievals were consistent between the two algorithms.The AMPR algorithm shows potential in retrieving aerosol optical properties over a vegetation surface.     

Analysis and evaluation of the global aerosol optical properties simulated by an online aerosol-coupled non-hydrostatic icosahedral atmospheric model

Aerosol optical properties are simulated using the Spectral Radiation Transport Model for Aerosol Species(SPRINTARS)coupled with the Non-hydrostatic ICosahedral Atmospheric Model(NICAM). The 3-year global mean all-sky aerosol optical thickness(AOT) at 550 nm, the ngstr m Exponent(AE) based on AOTs at 440 and 870 nm, and the single scattering albedo(SSA) at 550 nm are estimated at 0.123, 0.657 and 0.944, respectively. For each aerosol species, the mean AOT is within the range of the Aero Com models. Both the modeled all-sky and clear-sky results are compared with observations from the Moderate Resolution Imaging Spectroradiometer(MODIS) and the Aerosol Robotic Network(AERONET). The simulated spatiotemporal distributions of all-sky AOTs can generally reproduce the MODIS retrievals, and the correlation and model skill can be slightly improved using the clear-sky results over most land regions. The differences between clear-sky and all-sky AOTs are larger over polluted regions. Compared with observations from AERONET, the modeled and observed all-sky AOTs and AEs are generally in reasonable agreement, whereas the SSA variation is not well captured. Although the spatiotemporal distributions of all-sky and clear-sky results are similar, the clear-sky results are generally better correlated with the observations. The clear-sky AOT and SSA are generally lower than the all-sky results, especially in those regions where the aerosol chemical composition is contributed to mostly by sulfate aerosol. The modeled clear-sky AE is larger than the all-sky AE over those regions dominated by hydrophilic aerosol, while the opposite is found over regions dominated by hydrophobic aerosol.     

利用FY-4A卫星光学数据对中国近地面PM2.5浓度的估算和检验分析

对FY-4A卫星的气溶胶光学厚度（AOD）产品进行检验,并根据卫星相关观测资料,通过改进后的PMRS方法,反演得到中国近地面PM_2.5质量浓度网格化分布。结果表明,FY-4A卫星反演不同站点AOD与地基观测网（AERONET）观测结果吻合较好,但存在一定的低估或高估现象,相关系数区间为0.54—0.87。将细粒子比（FMF）以0.4为界进行划分,FMF＞0.4时,拟合结果较FMF≤0.4时更接近于AERONET观测结果;但FMF≤0.4时,卫星反演的AOD稳定性优于FMF＞0.4时。通过引入AOD的大小,改进FMF＞0.4时对细粒子柱状体积消光比（VE_f）的估算算法,并通过改进后的PMRS方法对中国近地面PM_2.5浓度进行逐时反演,其反演结果和地面观测结果相关较好,其中,乌鲁木齐、石家庄和徐州观测点的相关系数均高于0.7,但数值上仍存在高估或低估,误差结果由多种因素决定。空间分布中,卫星反演的中国2019年近地面PM_2.5浓度月均值与近地面观测的结果有较好的对应关系,二者逐月演变趋势基本一致,基本可以反映出中国近地面大气细粒子的空间分布,特别是秋、冬季京津冀周边区域、汾渭平原等污染高值区均与地面观测对应较好。      

Ship measurements of submicron aerosol size distributions over the Yellow Sea and the East China Sea

During the spring of 2005, the total particle concentrations and the submicron aerosol size distributions were measured on board the research vessel over the south sea of Korea and the Korean sector of the Yellow Sea. Similar measurements were made over the East China Sea in autumn 2005. The aerosol properties varied dynamically according to the meteorological conditions, the proximity to the land masses and the air mass back trajectories. The average total particle concentration was the lowest over the East China Sea, 4335 ± 2736 cm^− 3, but the instantaneous minimum, 837 cm^− 3, for the entire ship measurement was recorded during the Yellow Sea cruise. There was also a long (more than 6 h) stretch of low total particle concentrations that fell as low as 1025 cm^− 3 during the East China Sea cruise when the ship was the farthest from the shores and the air mass back trajectories resided long hours over the sea. These observations lead to the suggestion of ~ 1000 cm^− 3 as the background total particle concentration over the marine boundary layer in the studied region of the Yellow Sea and the East China Sea, implying significant anthropogenic influence even for the background value. In the mean time, average aerosol size distributions were unimodal and the mode diameter ranged between 52 and 86 nm, excluding the fog periods, which suggests that the aerosols measured in this study experienced relatively less aging processes within the marine boundary layer.     

Carbonaceous materials in size-segregated atmospheric aerosols from urban and coastal-rural areas at the Western European Coast

A high-volume cascade impactor, equipped with a PM10 inlet, was used to collect size-segregated aerosol samples during the summer of 2004 at two Portuguese locations: a coastal-rural area (Moitinhos) and an urban area (Oporto). Concentrations of airborne particulate matter (PM), total carbon (TC), organic carbon (OC), elemental carbon (EC), and water-soluble organic carbon (WSOC) were determined for the following particle size ranges: < 0.49, 0.49–0.95, 0.95–3.0, and 3.0–10 µm. The total PM mass concentrations at the urban and coastal-rural sites ranged from 22.8 to 79.6 μg m^− 3 and 19.9 to 28.2 μg m^− 3, respectively, and more than 56% of the total aerosol mass was found in the fractions below 3.0 μm. At both locations the highest concentrations of OC and EC were found in the submicrometer size range. The regional variability for the OC and EC concentrations, with the highest concentrations being found in the urban area, was related to the contribution of local primary sources (mostly traffic emissions). It was also verified an enrichment of the small size particles in WSOC, representing on average 37.3(± 12.4)% and 59.7(± 18.0)% of OC in the very fine aerosol at the coastal-rural and urban areas, respectively. The amount of secondary OC calculated by the minimum OC/EC ratio method indicates that secondary organic aerosol formation was important throughout the study at both sites. The obtained results suggest that long-range transport and favourable summer conditions for photochemical oxidation are key factors determining secondary OC formation in the coastal-rural and urban areas. The ultraviolet absorption properties of the chromophoric constituents of the WSOC fractions were also different among the different particle size ranges and also between the two sampling locations, thus suggesting the strong impact of the diverse emission sources into the composition of the size-segregated organic aerosol.     

Particulate contribution to extinction of visible radiation: Pollution, haze, and fog

A data set acquired by eight particle-dedicated instruments set up on the SIRTA (Site Instrumental de Recherche par Télédétection Atmosphérique, which is French for Instrumented Site for Atmospheric Remote Sensing Research) during the ParisFog field campaign are exploited to document microphysical properties of particles contributing to extinction of visible radiation in variable situations. The study focuses on a 48-hour period when atmospheric conditions are highly variable: relative humidity changes between 50 and 100%, visibility ranges between 65 and 35 000 m, the site is either downwind the Paris area either under maritime influence. A dense and homogeneous fog formed during the night by radiative cooling. In 6 h, visibility decreased down from 30 000 m in the clear-sky regime to 65 m within the fog, because of advected urban pollution (factor 3 to 4 in visibility reduction), aerosol hydration (factor 20) and aerosol activation (factor 6). Computations of aerosol optical properties, based on Mie theory, show that extinction in clear-sky regime is due equally to the ultrafine modes and to the accumulation mode. Extinction by haze is due to hydrated aerosol particles distributed in the accumulation mode, defined by a geometric mean diameter of 0.6 μm and a geometric standard deviation of 1.4. These hydrated aerosol particles still contribute by 20 ± 10% to extinction in the fog. The complementary extinction is due to fog droplets distributed around the geometric mean diameter of 3.2 μm with a geometric standard deviation of 1.5 during the first fog development stage. The study also shows that the experimental set-up could not count all fog droplets during the second and third fog development stages.     

大气气溶胶的卫星遥感及其在气候和环境研究中的应用

卫星遥感可以获得全球范围的大气气溶胶光学特性,目前国内外已有多颗卫星观测能够提供气溶胶特性的资料。本文综述性介绍国内外卫星遥感气溶胶特性方面的研究进展和成果,并讨论了卫星遥感资料在气候和环境研究领域中的应用。主要内容包括:极轨/静止卫星平台搭载的被动遥感传感器及其反演气溶胶特性的方法;星载激光雷达获取气溶胶光学特性的方法;国内外正在研发的新一代卫星主、被动气溶胶遥感探测器;卫星气溶胶产品在气溶胶辐射强迫、气候效应、大尺度污染输送、区域空气质量监测等研究中的应用。     

Characteristics of biomass burning aerosol and its impact on regional air quality in the summer of 2003 at Gwangju, Korea

The main objective of this study is to investigate the chemical characteristics of biomass burning aerosol and its impact on regional air quality during an agricultural waste burning period in early summer in the rural areas of Korea. A 12-h integrated intensive sampling of biomass burning aerosol in the fine and coarse modes was conducted on 2–20 June 2003 in Gwangju, Korea. The collected samples were analyzed for concentrations of mass, ionic, elemental, and carbonaceous species. Average concentrations of fine and coarse mass were measured to be 67.9 and 18.7 μg m^− 3 during the biomass burning period, 41.9 and 18.8 μg m^− 3 during the haze period, and 35.6 and 13.3 μg m^− 3 during the normal period, respectively. An exceptionally high PM_2.5 concentration of 110.3 μg m^− 3 with a PM_2.5/PM₁₀ ratio of 0.79 was observed on 6 June 2003 during the biomass burning period. The potassium ratio method was used to identify biomass burning samples. The average ratio of potassium in the fine mode to the coarse mode (FK/CK) was 23.8 during the biomass burning period, 6.0 during the haze period, and 4.7 during the normal period, respectively. A FK/CK ratio above 9.2 was considered a criterion for biomass burning event in this study. Particulate matter from the open field burning of agricultural waste has an adverse impact on visibility, human health, and regional air quality.     

北京等7个气象台站太阳总辐射观测资料的准确度评估

基于地面太阳短波总辐射对气溶胶光学特性和地表反照率的敏感性, 该文提出了一个评估我国气象台站总辐射资料准确度的方法。该方法选用气溶胶光学厚度和太阳天顶角较小情形下的晴天辐射资料, 从太阳直射辐射反演气溶胶光学厚度, 用于计算宽带透过率, 再从该透过率和总辐射资料反演太阳常数E_{0, P}, 并采用E_{0, P}对世界辐射基准 (WRR) 的偏差表示总辐射资料的不确定性。模拟结果表明:气溶胶折射率虚部和大气柱水汽含量的输入误差是两个主要的评估不确定因子。用于准确度评估的资料越多, 越有利于平滑气溶胶、水汽含量等输入参数随机误差的效应, 评估结果越合理。应用这一方法, 该文评估了2000— 2004年我国沈阳、额济纳旗、北京、乌鲁木齐、格尔木、上海和广州7个气象台站总辐射资料的准确度。7个站共有1161个太阳常数反演值, 都满足太阳天顶角余弦 (μ₀) 大于0.7的条件。这些E_{0, P}值对WRR的最大偏差为7.33%, 97.78%的E_{0, P}值对WRR的偏差小于5%, 总平均E_{0, P}值对WRR偏差只有-1.15 %。依据这些结果, 当μ₀≥0.7时, 这些台站的晴天总辐射资料的不确定度估计为5%。     

Scavenging of atmospheric ions and aerosols by drifting snow in Antarctica

Measurements of the small-, intermediate-, and large-ion concentrations and the air–earth current density along with simultaneous measurements of the concentration and size distribution of aerosol particles in the size ranges 4.4–163 nm and 0.5–20 μm diameter are reported for a drifting snow period after the occurrence of a blizzard at a coastal station, Maitri, Antarctica. Ion concentrations of all categories and the air–earth current simultaneously decrease by approximately an order of magnitude as the wind speed increases from 5 to 10 ms^− 1. The rate of decrease is the highest for large ions, lowest for small ions and in-between the two for intermediate ions. Total aerosol number concentration decreases in the 4.4–163 nm size range but increases in the 0.5–20 μm size range with wind speed. The size distribution of the nanometer particles shows a dominant maximum at ~ 30 nm diameter throughout the period of observations and the height of the maximum decreases with wind speed. However, larger particles show a maximum at ~ 0.7 μm diameter but the height of the maximum increases with increasing wind speed. The results are explained in terms of scavenging of atmospheric ions and aerosols by the drifting snow particles.     

On Eastern Asian Dust Storm

In this paper, the characteristics of eastern Asian dust storm are examined with emphasis on the satellite measurements of aerosol optical thickness. The reflectivity of solar radiation from the earth’s atmosphere depends on the optical thickness. The satellite measurement of radiance of sunlight, scattered by the earth and its atmosphere, is used to derive the properties of aerosol on oceanic surfaces. This paper involves the following: (1) investigation of the measurement of dust storm over the oceanic surface by GMS satellite; (2) investigation of the measurement of dust storm over the land surface by ground-based instruments such as actinometer, lidar, etc.; (3) for comparison, de-riving an atmospheric aerosol size distribution over the oceanic surface of calm weather through measurements of NOAA satellite; and (4) the weather process and its mass load of eastern Asian dust storm.     

One year measurements of aerosol optical properties over an urban coastal site: Effect on local direct radiative forcing

We present results of direct aerosol radiative forcing over a French Mediterranean coastal zone based on one year of continuous observations of aerosol optical properties during 2005–2006. Monthly-mean aerosol optical depth at 440 nm ranged between 0.1 and 0.34, with high Angstrom coefficient (α > 1.2). The single scattering albedo (at 525 nm) estimated at the surface ranged between 0.7 and 0.8, indicating significant absorption. The presence of aerosols over the Mediterranean zone during summer decreases the shortwave radiation reaching the surface by as much as 26 ± 3.9 W m^− 2, and increases the top of the atmosphere reflected radiation by as much as 5.2 ± 1.0 W m^− 2. The shortwave atmospheric absorption translates to an atmospheric heating of 2.5 to 4.6 K day^− 1. Concerted efforts are needed for investigating the possible impact of the increase in heating rate on the maintenance of heat-waves frequently occurring over this coastal region during summer time.     

Comparison of cloud-top height retrievals from ground-based 35 GHz MMCR and GMS-5 satellite observations at ARM TWP Manus site

Retrievals of cloud-top heights from the ARM 35 GHz Millimeter Wave Cloud Radar (MMCR) located on Manus Island are compared to those from the GMS-5 satellite as a means to evaluate the accuracy of both MMCR and GMS-5 retrievals, as well as to ascertain their limitations. Comparisons are carried out for retrievals of both single-layer and multilayer clouds as seen by radar, but only for satellite-detected clouds with 100% amount within a 0.3×0.3° domain centered at the ARM site of one cloud type (i.e., low, middle, or high). Mean differences, with 95% confidence limits, between radar- and satellite-retrieved cloud-top heights (i.e., radar-retrieved cloud-top heights−satellite-retrieved cloud-top heights) are 0.3±0.3 km for single-layer clouds and −0.7±0.3 km for multilayer clouds. The study reveals that for thick clouds (i.e., cloud base ≤1 km and cloud thickness ≥10 km), which are representative of convective towers with no/light precipitation as well as thick anvil clouds, retrievals from the MMCR agree well with those from satellite with mean differences of 0.0±0.4 and −0.2±0.3 km for single-layer and multilayer clouds, respectively. For clouds of lesser thickness, mean cloud-top heights derived from satellite are lower than those derived from radar by as much as 2.0 km. It is also shown that for convective clouds with heavy precipitation, MMCR retrievals underestimate the cloud-top heights significantly.     

Changes in integral and aerosol atmospheric turbidity in Trans-Baikal and Central Siberia

The analysis of time series of the Linke turbidity factors is performed for the atmosphere mass m = 2 (T ₂) and atmospheric aerosol optical thickness for the wavelength λ₀ = 0.55 μm (AOT) from the data of 14 actinometrical stations of Central Siberia and Trans-Baikal territory. It is shown that over the period from 1976 to 2006, the increased atmospheric transparency is observed in the region. Quantitative estimates of changes in multiyear mean annual variations of T ₂ and AOT at different periods of averaging and for different time periods are derived.