An efficient method for computing atmospheric radiances in clear-sky and cloudy conditions

A computationally efficient method is developed to simulate the radiances in a scattering and absorbing atmosphere along an arbitrary path in the spectral region ranging from visible to far-infrared with a spectral resolution of 1 cm⁻¹. For a given spectral region, the method is based on fitting radiances pre-calculated from the discrete ordinate radiative transfer (DISORT) at several wavenumbers. Radiances at other wavenumbers are interpolated based on the pre-computed total absorption and scattering optical thicknesses and the surface albedo. The computational efficiency and accuracy of the method are tested in comparison with rigorous simulations for various scenarios under the same conditions. For both clear-sky and cloud atmospheres, the present method is at least 140 times faster than the direct application of DISORT. Across the spectral range, the standard relative differences between the new method and the DISORT are less than 2% for clear-sky conditions. Root-mean-square (RMS) differences of the top of the atmosphere (TOA) brightness temperatures between the new method and DISORT, for atmospheric infrared sounder (AIRS) channels over clear-sky, ice cloudy and water cloudy skies, are within the noise equivalent differential temperature (NEDT) of the AIRS sensor. The fast method is also applied to simulations of the spectral downwelling radiance measured by the Fourier transform infrared (FTIR) interferometer, and to the simulations of the AIRS upwelling radiances under clear-sky and cloudy conditions.     

A fast infrared radiative transfer model for overlapping clouds

A fast infrared radiative transfer model (FIRTM2) appropriate for application to both single-layered and overlapping cloud situations is developed for simulating the outgoing infrared spectral radiance at the top of the atmosphere (TOA). In FIRTM2 a pre-computed library of cloud reflectance and transmittance values is employed to account for one or two cloud layers, whereas the background atmospheric optical thickness due to gaseous absorption can be computed from a clear-sky radiative transfer model. FIRTM2 is applicable to three atmospheric conditions: (1) clear-sky, (2) single-layered ice or water cloud, and (3) two simultaneous cloud layers in a column (e.g., ice cloud overlying water cloud). Moreover, FIRTM2 outputs the derivatives (i.e., Jacobians) of the TOA brightness temperature with respect to cloud optical thickness and effective particle size. Sensitivity analyses have been carried out to assess the performance of FIRTM2 for two spectral regions, namely the longwave (LW) band (587.3-1179.5 cm⁻¹) and the short-to-medium wave (SMW) band (1180.1-2228.9 cm⁻¹). The assessment is carried out in terms of brightness temperature differences (BTD) between FIRTM2 and the well-known discrete ordinates radiative transfer model (DISORT), henceforth referred to as BTD (F−D). The BTD (F−D) values for single-layered clouds are generally less than 0.8 K. For the case of two cloud layers (specifically ice cloud over water cloud), the BTD (F−D) values are also generally less than 0.8 K except for the SMW band for the case of a very high altitude (>15 km) cloud comprised of small ice particles. Note that for clear-sky atmospheres, FIRTM2 reduces to the clear-sky radiative transfer model that is incorporated into FIRTM2, and the errors in this case are essentially those of the clear-sky radiative transfer model.     

A fast infrared radiative transfer model based on the adding-doubling method for hyperspectral remote-sensing applications

A fast infrared radiative transfer (RT) model is developed on the basis of the adding-doubling principle, hereafter referred to as FIRTM-AD, to facilitate the forward RT simulations involved in hyperspectral remote-sensing applications under cloudy-sky conditions. A pre-computed look-up table (LUT) of the bidirectional reflection and transmission functions and emissivities of ice clouds in conjunction with efficient interpolation schemes is used in FIRTM-AD to alleviate the computational burden of the doubling process. FIRTM-AD is applicable to a variety of cloud conditions, including vertically inhomogeneous or multilayered clouds. In particular, this RT model is suitable for the computation of high-spectral-resolution radiance and brightness temperature (BT) spectra at both the top-of-atmosphere and surface, and thus is useful for satellite and ground-based hyperspectral sensors. In terms of computer CPU time, FIRTM-AD is approximately 100-250 times faster than the well-known discrete-ordinate (DISORT) RT model for the same conditions. The errors of FIRTM-AD, specified as root-mean-square (RMS) BT differences with respect to their DISORT counterparts, are generally smaller than 0.1 K.     

卷云短波红外辐射特性

 采用离散纵标法耦合大气分子吸收，模拟计算了卷云大气的反射特性。研究了在短波波段卷云辐射性质随波长、卷云光学厚度、卷云有效尺度、云高和卷云中冰晶粒子形状等的变化关系，分析了卷云对大气红外背景辐射的影响。结果表明：在2.7 μm的水汽强吸收带上，卷云的出现明显增强了该波段的大气背景辐射，反射率随光学厚度和云高增大而增大。     

AIRS红外高光谱卫星数据反演卷云光学厚度和云顶高度

基于大气红外探测器L1B红外高光谱辐射观测资料,结合中分辨率成像光谱仪(moderate resolution imaging spectroradiometer, MODIS)云产品数据,利用通用大气辐射传输模式(combined atmospheric radiative transfer model,CART),根据模式模拟和AIRS实际观测亮温的亮温差,研究从AIRS红外波段1 070～1 135 cm-1高光谱数据反演卷云的光学厚度和云顶高度。将反演的卷云光学厚度与云顶高度作为输入参数模拟计算650～1 150 cm-1波段卷云大气顶的辐射亮温谱,并将模拟值与AIRS观测亮温谱进行了对比分析。将反演的卷云光学厚度和云顶高度和AIRS的760通道(900.56 cm-1,11.1 μm)的亮温以及MODIS卷云反射率进行了对比分析。最后将反演的卷云云顶高度和MODIS云顶高度进行了对比分析。研究结果表明：反演所使用的650～1 150 cm-1波段模式模拟和观测亮温谱吻合得很好,说明CART可以较好的模拟AIRS亮温谱。反演的卷云参数与AIRS在大气窗口区的760通道(900.56 cm-1,11.1 μm)的亮温的分布满足低亮温对应较大的卷云光学厚度和高云顶高度。反演的卷云参数和MODIS卷云的反射率分布满足高卷云光学厚度和云顶高度对应高卷云反射率。反演的卷云云顶高度和MODIS的卷云云顶高度之间线性相关系数相对较高,且都在8.5～11.5 km的概率较高,两者的概率分布趋势一致。说明CART可以用于反演卷云的性质,反演结果具有一定的可靠性。     

Radiative effect differences between multi-layered and single-layer clouds derived from CERES, CALIPSO, and CloudSat data

Clouds alter general circulation through modification of the radiative heating profile within the atmosphere. Their effects are complex and depend on height, vertical structure, and phase. The instantaneous cloud radiative effect (CRE) induced by multi-layered (ML) and single-layer (SL) clouds is estimated by analyzing data collected by the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO), CloudSat, and Clouds and Earth’s Radiation Energy Budget System (CERES) missions from March 2007 through February 2008. The CRE differences between ML and SL clouds at the top of the atmosphere (TOA) and at the surface were also examined. The zonal mean shortwave (SW) CRE differences between the ML and SL clouds at the TOA and surface were positive at most latitudes, peaking at 120 W m⁻² in the tropics and dropping to −30 W m⁻² at higher latitudes. This indicated that the ML clouds usually reflected less sunlight at the TOA and transmitted more to the surface than the SL clouds, due to their higher cloud top heights. The zonal mean longwave (LW) CRE differences between ML and SL clouds at the TOA and surface were relatively small, ranging from −30 to 30 W m⁻². This showed that the ML clouds only increased the amount of thermal radiation at the TOA relative to the SL clouds in the tropics, decreasing it elsewhere. In other words, ML clouds tended to cool the atmosphere in the tropics and warm it elsewhere when compared to SL clouds. The zonal mean net CRE differences were positive at most latitudes and dominated by the SW CRE differences.     

大气折射对可见光波段辐射传输特性的影响

折射是影响辐射传输的重要因素. 为分析大气折射对辐射传输的影响, 基于Monte Carlo方法, 给出了考虑大气折射的矢量辐射传输模型, 实现了均匀气层和耦合面处光子随机运动过程的模拟, 实现了直射光及漫射光Stokes矢量、偏振度和辐射通量等参数的计算. 在考虑和不考虑大气折射两种条件下, 验证了模型的准确性; 在纯瑞利散射条件下, 讨论了大气折射对不同方向漫射光Stokes矢量的影响; 在不同太阳天顶角、大气廓线、气溶胶及含云大气条件下, 分析了大气折射对辐射传输过程的影响. 结果表明: 大气折射对漫射光Stokes矢量的影响主要体现在天顶角70°–110°区间, 且随着太阳入射角增大, 其影响更为显著; 不同大气廓线情形下, 大气折射对Stokes矢量的影响不一致, 其原因是不同大气廓线对应的折射率廓线存在差异. 含云及含气溶胶大气条件下, 大气折射对辐射传输的影响变弱, 沙尘型及海盐型气溶胶条件下, 折射对辐射传输的影响强于可溶型气溶胶情形; 不同形状气溶胶条件下, 大气折射对辐射传输的影响也存在显著差异; 不同云高条件下, 大气折射对漫射光Stokes矢量的影响无显著差异, 但随着云光学厚度增大, 大气折射的影响减弱.     

Comparison of single and multiple scattering approaches for the simulation of limb-emission observations in the mid-IR

The validity of single scattering radiative transfer calculations for simulation of limb-emission measurements of clouds in the mid-infrared spectral region was investigated by comparison with a multiple scattering model. For in limb direction optically thin clouds, like polar stratospheric clouds, errors of the single scattering scheme range below 3%. For optically thick clouds deviations are below 3% in case of low single scattering albedo (ω₀=0.24) increasing up to 10-30% for ω₀=0.84. Clouds which are optically thick in limb, but thin in nadir direction, can cause limb radiances which are by a factor of 1.7 higher than the blackbody radiance at cloud altitude.     

Cloud 3D effects on broadband heating rate profiles: I. Model simulation

Solar broadband heating directly drives the atmospheric and ocean circulations, and is largely determined by cloud spatial 3-diminesional (3D) structures. To study the cloud 3D effects on radiation, a 3D broadband Monte-Carlo radiative transfer model, along with an Independent Pixel/Column Approximation (IPA) method, is used to simulate radiation and heating rate of three typical cloud fields generated by cloud resolving models (CRM). A quantitative and statistical estimation of cloud 3D effects has been developed to investigate the impact of cloud 3D structures on both heating rate strength, STD_Bias, and vertical distribution, CorrCoef. The cloud 3D structures affect some clouds more in heating rate strength and others more in vertical distribution. It is crucial to use the combination of CorrCoef and STD_Bias for better quantitative evaluation of the 3D effects. Furthermore, there is no simple way to define a critical resolution (or average radius), within which the IPA heating rate profiles closely represent the true 3D heating rate profiles. The critical radius (or resolution) strongly depends on solar incident angle as well as cloud vertical distribution. Also, the critical radii for clear-sky columns are larger than for cloudy columns, although the corresponding STD_Bias for clear-sky columns are smaller than for cloudy columns. Analysis based on two different statistical average methods illustrates that the cloud 3D effects due to the dimensionality difference between the 3D clouds (circle average) and 2D clouds (line average) significantly impact on the heating rate profiles.     

Retrieval of tropospheric NO2 columns from satellite measurements in presence of cirrus: A theoretical sensitivity study using SCIATRAN and prospect application for the A-Train

A theoretical sensitivity study of the influence of cirrus cloud properties on tropospheric NO₂ columns retrieved from the spaceborne Ozone Monitoring Instrument (OMI) measurements is performed. It is conducted within the framework of the synergetic use of A-Train sensors to derive more representative trace gas products. We aim to study the potential effects of cirrus clouds on tropospheric NO₂ retrievals using a retrieval algorithm that, unlike the OMI Standard and DOMINO algorithms, does not correct for the effects of clouds. The sensitivity study is based on the radiative transfer code SCIATRAN that performs both simulations of top of atmosphere (TOA) reflectances as measured by an OMI-like band and tropospheric NO₂ column retrievals based on the differential optical absorption spectroscopy (DOAS) method. The results of the sensitivity study show that if a correction for cirrus clouds is not included in our simple retrieval that does not account for clouds in the first place, the tropospheric column can be underestimated by 55%. This underestimation depends strongly on cirrus parameters as, in order of importance, cloud fraction, cloud optical depth, asymmetry factor of cirrus cloud phase function and cloud top height. The perspective of the synergy between OMI and cloud information obtained from cloud-derived products of the A-Train is evaluated in two parts by applying a simple cloud correction scheme based on the independent pixel approximation (IPA). Firstly, we evaluated the tropospheric NO₂ column retrievals error caused by uncertainties in cirrus cloud properties. Secondly we studied the influence of subpixel cloud optical depth variability on NO₂ retrievals. From our simulations, it is demonstrated that the error will be reduced significantly if the cloud fraction is lower or equal to 0.5. In this case, the cloud fraction and the cloud optical depth must be known within accuracy less than 0.05% and 50%, respectively. The cloud top height and the asymmetry factor must be known within uncertainty of at least 1 km and less than 0.05, respectively. The latter result shows that the uncertainty of the asymmetry factor is a major source of error in the cloud correction for tropospheric NO₂ retrieval in the presence of cirrus.     

Estimates of radiation over clouds and dust aerosols: Optimized number of terms in phase function expansion

The bulk-scattering properties of dust aerosols and clouds are computed for the community radiative transfer model (CRTM) that is a flagship effort of the Joint Center for Satellite Data Assimilation (JCSDA). The delta-fit method is employed to truncate the forward peaks of the scattering phase functions and to compute the Legendre expansion coefficients for re-constructing the truncated phase function. Use of more terms in the expansion gives more accurate re-construction of the phase function, but the issue remains as to how many terms are necessary for different applications. To explore this issue further, the bidirectional reflectances associated with dust aerosols, water clouds, and ice clouds are simulated with various numbers of Legendre expansion terms. To have relative numerical errors smaller than 5%, the present analyses indicate that, in the visible spectrum, 16 Legendre polynomials should be used for dust aerosols, while 32 Legendre expansion terms should be used for both water and ice clouds. In the infrared spectrum, the brightness temperatures at the top of the atmosphere are computed by using the scattering properties of dust aerosols, water clouds and ice clouds. Although small differences of brightness temperatures compared with the counterparts computed with 4, 8, 128 expansion terms are observed at large viewing angles for each layer, it is shown that 4 terms of Legendre polynomials are sufficient in the radiative transfer computation at infrared wavelengths for practical applications.     

Infrared radiative transfer modelling in a 3D scattering cloudy atmosphere: Application to limb sounding measurements of cirrus

The Monte Carlo cloud scattering forward model (McClouds_FM) has been developed to simulate limb radiative transfer in the presence of cirrus clouds, for the purposes of simulating cloud contaminated measurements made by an infrared limb sounding instrument, e.g. the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS). A reverse method three-dimensional Monte Carlo transfer model is combined with a line-by-line model for radiative transfer through the non-cloudy atmosphere to explicitly account for the effects of multiple scattering by the clouds. The ice cloud microphysics are characterised by a size distribution of randomly oriented ice crystals, with the single scattering properties of the distribution determined by accurate calculations accounting for non-spherical habit.A comparison of McClouds_FM simulations and real MIPAS spectra of cirrus shows good agreement. Of particular interest are several noticeable spectral features (i.e. H₂O absorption lines) in the data that are replicated in the simulations: these can only be explained by upwelling tropospheric radiation scattered into the line-of-sight by the cloud ice particles.     

A simple new radiative transfer model for simulating the effect of cirrus clouds in the microwave spectral region

The upwelling atmospheric radiation in the millimeter wave spectral range is influenced by the presence of cirrus clouds. A plane parallel radiative transfer model which can take into account the effect of multiple scattering by ice particles in the cirrus has been developed and is used to simulate the brightness temperatures as they would be measured by a satellite instrument. The model uses an iterative procedure to solve the radiative transfer equation. The formulation of the model is such that it can easily be adapted to treat the full specific intensity vector instead of just the scalar total intensity. A convergence test for the model is explained and two cirrus cloud scenarios are simulated. The results illustrate the linearity of microwave radiative transfer for not too strong cirrus clouds in this frequency region.     

A Monte Carlo method for 3D thermal infrared radiative transfer

A 3D Monte Carlo model for specific application to the broadband thermal radiative transfer has been developed in which the emissivities for gases and cloud particles are parameterized by using a single cubic element as the building block in 3D space. For spectral integration in the thermal infrared, the correlated k-distribution method has been used for the sorting of gaseous absorption lines in multiple-scattering atmospheres involving 3D clouds. To check the Monte-Carlo simulation, we compare a variety of 1D broadband atmospheric fluxes and heating rates to those computed from the conventional plane-parallel (PP) model and demonstrate excellent agreement between the two. Comparisons of the Monte Carlo results for broadband thermal cooling rates in 3D clouds to those computed from the delta-diffusion approximation for 3D radiative transfer and the independent pixel-by-pixel approximation are subsequently carried out to understand the relative merits of these approaches.     

Sensitivity of atmospheric-surface parameters retrieval to the spectral stability of channels in thermal IR

Sensitivity of the solutions of forward and inverse problems of the atmospheric-surface parameters retrieval to spectral shifts of channels is considered. The solution of the forward problem is obtained by radiative transfer simulation. The retrieval (solution of the inverse problem) is obtained by linear (optimal interpolation) and non-linear (variational) techniques. It is shown that atmospheric temperature profiles exhibit high sensitivity to the spectral shift, while the humidity profiles are moderately sensitive while the sea surface temperatures retrievals are insensitive. Two approaches are proposed to reduce the effect of channel spectral shift, one is based on channel selection and the other approach is related to proper calibration of the cost function. We performed the numerical simulations using the parameters of AIRS spectrometer to illustrate the sensitivity of forward and inverse problems. The results of the simulation show that the inversion error can be significantly reduced by the proposed techniques.     

One-dimensional solar radiative transfer: Perturbation approach and its application to independent-pixel calculations for realistic cloud fields

The radiative transfer perturbation theory (RTPT), which has already been introduced in atmospheric radiative transfer several years ago, is applied to cloud related problems. The RTPT requires the solution of the radiative transfer equation in the forward and the adjoint mode. The basic principles of this technique are presented as well as its extensions to isotropic surface reflection and its conjunction with the Hermite interpolation. This set of methods is applied to different atmospheric conditions including realistic cloud scenes. The results are compared with the usual (forward) independent-pixel calculations with respect to errors of individual pixels and domain-averaged values. The RTPT turns out to be sufficiently accurate in the case the clouds’ internal vertical variations remain moderate. It is also shown that, depending on the specific radiative transfer problem, the RTPT can offer some advantages on computational speed. However, the limitations of the RTPT with regard to realistic clouds are addressed as well.     

Scattering in thick multifractal clouds, Part II: Multiple scattering

In Part I of this paper, we developed asymptotic approximations for single photon scattering in thick, highly heterogeneous, “Log-Lévy” multifractal clouds. In Part II, theoretical multiple scattering predictions are numerically tested using Monte Carlo techniques, which show that, due to long range correlations, the photon paths are “subdiffusive” with the corresponding fractal dimensions tending to increase slowly with mean optical thickness. We develop reasonably accurate statistical relations between N scatter statistics in thick clouds and single scatter statistics in thin clouds. This is explored further using discrete angle radiative transfer (DART) approach in which the radiances decouple into non-interacting families with only four (for 2-D clouds) radiance directions each. Sparse matrix techniques allow for rapid and extremely accurate solutions for the transfer; the accuracy is only limited by the spatial discretization.By “renormalizing” the cloud density, we relate the mean transmission statistics to those of an equivalent homogeneous cloud. This simple idea is remarkably effective because two complicating effects act in contrary directions: the “holes” which lead to increased single scatter transmission and the tendency for multiply scattered photons to become “trapped” in optically dense regions, thus decreasing the overall transmission.     

大气对星载被动微波影响分析研究

被动微波遥感具有全天候工作的能力,但是在不同的大气状态下被动微波遥感受大气的影响不同。为了研究大气对高级微波扫描辐射计AMSR-E (advanced microwave scanning radiometer-earth observing system)入瞳亮温的影响,分别采用晴空和典型层云大气数据作为微波辐射传输模型的输入,进行大气微波辐射信号的模拟工作并分析大气的影响。结果表明晴空下大气水汽是引起大气辐射的主要因素,晴空条件下大气对典型被动微波传感器低频的(<18.7 GHz)透过率大于0.98,在整个辐射传输过程中可以忽略不计。36.5和89 GHz的大气透过率在晴空下分别为0.896和0.756,在用微波高频通道进行陆表参数反演时需进行大气水汽影响的校正; 云覆盖条件或者阴天情况下云中液态水是引起大气辐射的主要因素,典型层云覆盖下大气的透过率在10.7,18.7和36.5 GHz分别为0.942,0.828和0.605。与晴空相比,由层云中液态水引起的大气下行辐射的增量在36.5 GHz最大达到75.365 K。表明在云覆盖时大气影响的校正过程中云层的影响是校正重点。最后利用大气探空数据计算了内蒙古海拉尔地区2013年夏季7月份的大气透过率,结果显示C、X波段的大气透过率接近1,89 GHz受水汽影响较大,其地球表层大气透过率不超过0.7。在内蒙古海拉尔地区,夏季大气透过率具有较为稳定的值,但是随着局部水汽的变化具有0.1左右的波动。     

Effects of sea surface temperature, cloud radiative and microphysical processes, and diurnal variations on rainfall in equilibrium cloud-resolving model simulations

The effects of sea surface temperature(SST),cloud radiative and microphysical processes,and diurnal variations on rainfall statistics are documented with grid data from the two-dimensional equilibrium cloud-resolving model simulations.For a rain rate of higher than 3 mm.h 1,water vapor convergence prevails.The rainfall amount decreases with the decrease of SST from 29℃ to 27℃,the inclusion of diurnal variation of SST,or the exclusion of microphysical effects of ice clouds and radiative effects of water clouds,which are primarily associated with the decreases in water vapor convergence.However,the amount of rainfall increases with the increase of SST from 29℃ to 31℃,the exclusion of diurnal variation of solar zenith angle,and the exclusion of the radiative effects of ice clouds,which are primarily related to increases in water vapor convergence.For a rain rate of less than 3 mm.h 1,water vapor divergence prevails.Unlike rainfall statistics for rain rates of higher than 3 mm.h 1,the decrease of SST from 29℃ to 27℃ and the exclusion of radiative effects of water clouds in the presence of radiative effects of ice clouds increase the rainfall amount,which corresponds to the suppression in water vapor divergence.The exclusion of microphysical effects of ice clouds decreases the amount of rainfall,which corresponds to the enhancement in water vapor divergence.The amount of rainfall is less sensitive to the increase of SST from 29℃ to 31℃ and to the radiative effects of water clouds in the absence of the radiative effects of ice clouds.     

Matrix formulations of radiative transfer including the polarization effect in a coupled atmosphere-ocean system

A vector radiative transfer model has been developed for a coupled atmosphere-ocean system. The radiative transfer scheme is based on the discrete ordinate and matrix operator methods. The reflection/transmission matrices and source vectors are obtained for each atmospheric or oceanic layer through the discrete ordinate solution. The vertically inhomogeneous system is constructed using the matrix operator method, which combines the radiative interaction between the layers. This radiative transfer scheme is flexible for a vertically inhomogeneous system including the oceanic layers as well as the ocean surface. Compared with the benchmark results, the computational error attributable to the radiative transfer scheme has been less than 0.1% in the case of eight discrete ordinate directions. Furthermore, increasing the number of discrete ordinate directions has produced computations with higher accuracy. Based on our radiative transfer scheme, simulations of sun glint radiation have been presented for wavelengths of 670 nm and 1.6 μm. Results of simulations have shown reasonable characteristics of the sun glint radiation such as the strongly peaked, but slightly smoothed radiation by the rough ocean surface and depolarization through multiple scattering by the aerosol-loaded atmosphere. The radiative transfer scheme of this paper has been implemented to the numerical model named Pstar as one of the OpenCLASTR/STAR radiative transfer code systems, which are widely applied to many radiative transfer problems, including the polarization effect.