Discrete Ordinate Radiative Transfer Research Articles

An improved BRDF hotspot model and its use in VLIDORT for studying the impact of atmospheric scattering on hotspot directional signatures in the atmosphere

Abstract. The term “hotspot” refers to the sharp increase in the reflectance occurring when incident (solar) and reflected (viewing) directions almost coincide in the backscatter direction. The accurate simulation of hotspot directional signatures is important for many remote sensing applications. The RossThick–LiSparse–Reciprocal (RTLSR) bidirectional reflectance distribution function (BRDF) model is widely used in radiative transfer simulations, and the hotspot model mostly used is from Maignan–Bréon, but it typically requires large values of numerical quadrature and Fourier expansion terms in order to represent the hotspot accurately for its use coupled with atmospheric radiative transfer modeling (RTM). In this paper, we have developed a modified version based on the Maignan–Bréon's hotspot BRDF model that converges much faster numerically, making it more practical for use in the RTMs that require Fourier expansion of BRDF to simulate the top-of-atmosphere (TOA) hotspot signatures, such as in the RTM models using the Doubling–Adding or discrete ordinate method. Using the vector linearized discrete ordinate radiative transfer model (VLIDORT), we found that reasonable TOA–hotspot accuracy can be obtained with just 23 Fourier terms for clear atmosphere and 63 Fourier terms for atmosphere with aerosol scattering. In order to study the impact of molecular and aerosol scattering on hotspot signatures, we carried out a number of hotspot signature simulations with VLIDORT. We confirmed that (1) atmospheric molecule scattering and the existence of aerosol tend to smooth out the hotspot signature at the TOA and that (2) the hotspot signature at the TOA in the near-infrared is larger than in the visible, and its impact by surface reflectance is more significant. As the hotspot amplitude at the TOA with aerosol scattering included is smaller than that with molecular scattering only, the amplitude of hotspot signature at the surface is likely underestimated in the previous analysis based on the POLDER measurements, where the atmospheric correction was based on a single-scatter Rayleigh-only calculation. This modified model can calculate the amplitude of the hotspot accurately, and, as it agrees very well with the original RossThick model away from the hotspot region, this model can be simply used in conditions with and without hotspots. However, there are some differences in this modified model compared to the original Maignan–Bréon model for the scattering angles close to the hotspot point; thus, it may not be appropriate for those who need an exact representation of the hotspot angular signature.

Assessment of aerosol optical and physical properties and implications for radiative effects over the semiarid region of Indo‐Gangetic Basin

This study assesses the physical and optical properties and estimated the radiative forcing of aerosol at Agra over the Indo‐Gangetic Basin (IGB) during July 2016–December 2019 using black carbon (BC) mass concentration (AE‐33 aethalometer), data sets from satellite and model simulations. The optical properties of aerosol and radiative forcing have been measured by the Optical and Physical Properties of Aerosols and Clouds (OPAC) and Santa Barbara Discrete Ordinate Radiative Transfer Atmospheric Radiative Transfer (SBDART) model. The high BC mass concentration has been observed in November and lowest in August. An adverse meteorological condition due to a combination of temperature and low wind speed results in poor dispersion in the wintertime is a common factor for high concentration level pollutants over Agra. The diurnal and temporal cycle of BC mass concentration exhibits a high concentration at nighttime due to the lower atmospheric boundary layer. The seasonal variation of absorption coefficient (βabs) and Absorption Angstrom Exponent (AAE) is found to be higher during post‐monsoon and lowest in monsoon season. This suggests that black carbon concentration over Agra is mainly generated from crop burning, waste burning, automobile exhaust and long‐range transport from Punjab and Haryana as the present site is downwind. OPAC‐derived aerosol optical depth (AOD), single‐scattering albedo (SSA), Angstrom Exponent (AE) and asymmetry parameter (AsyP) were estimated to be 0.57 ± 0.07, 0.78 ± 0.16, 0.99 ± 0.21 and 0.81 ± 0.15, respectively. AOD and AE from the OPAC and the moderate resolution imaging spectroradiometer (MODIS) have shown the consistent relationship. The mean radiative forcing is 18.3 ± 2.1 W m−2 at the top of the atmosphere while, at the surface, net radiative forcing is −42.4 ± 7.2 and 59.1 ± 6.5 W m−2 at the atmosphere during the study period. Vertical profiles were estimated using the observations from Cloud‐Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) satellite and the change in heating rate from the SBDART model over Agra.

Integrated efficient radiative transfer model named Dayu for simulating the imager measurements in cloudy atmospheres.

Rapid radiative transfer models are crucial to remote sensing and data assimilation. An integrated efficient radiative transfer model named Dayu, which is an updated version of the Efficient Radiative Transfer Model (ERTM) is developed to simulate the imager measurements in cloudy atmospheres. In Dayu model, the Optimized alternate Mapping Correlated K-Distribution model (OMCKD) which is predominant in dealing with the overlap of multiple gaseous lines is employed to efficiently calculate the gaseous absorption. The cloud and aerosol optical properties are pre-calculated and parameterized by the particle effective radius or length. Specifically, the ice crystal model is assumed as a solid hexagonal column, of which the parameters are determined based on massive aircraft observations. For the radiative transfer solver, the original 4-stream Discrete ordinate aDding Approximation (4-DDA) is extended to 2N-DDA (2N is the number of streams) which can calculate not only the azimuthally dependent radiance in the solar spectrum (including solar and infrared spectra overlap) but also the azimuthally averaged radiance in the thermal infrared spectrum through a unified adding method. Then the accuracy and efficiency of Dayu model are evaluated by comparing it with the benchmark model, i.e., Line-By-Line Radiative Transfer Model (LBLRTM) and DIScrete Ordinate Radiative Transfer (DISORT). Under the standard atmospheric profile, the maximum relative biases between Dayu model with 8-DDA / 16-DDA and the benchmark model (OMCKD with 64-stream DISORT) are 7.63% / 2.62% at solar channels but decreased to 2.66% / 1.39% at spectra-overlapping channel (3.7 μm). The computational efficiency of Dayu model with 8-DDA / 16-DDA is approximately three / two orders of magnitude higher than that of the benchmark model. At thermal infrared channels, the brightness temperature (BT) differences between Dayu model with 4-DDA and the benchmark model (LBLRTM with 64-stream DISORT) are bounded by 0.65K. Compared to the benchmark model, Dayu model with 4-DDA improves the computational efficiency by five orders of magnitude. In the application to the practical Typhoon Lekima case, the simulated reflectances and BTs by Dayu model have a high consistency with the imager measurements, demonstrating the superior performance of Dayu model in satellite simulation.

Insights into 3D cloud radiative transfer effects for the Orbiting Carbon Observatory

Abstract. Clouds impose radiance perturbations upon Orbiting Carbon Observatory (OCO-2)-measured spectra. The Spherical Harmonic Discrete Ordinate radiative transfer Method (SHDOM) code is applied in both idealized bar cloud and scene-specific calculations of 1D and 3D radiances in order to understand 3D cloud effects for a wide range of gas vertical optical depths and solar- and sensor-viewing geometries for ocean and land scenes. SHDOM calculations for 36 scenes over the Amazon and the Pacific are co-analyzed with Moderate Resolution Imaging Spectroradiometer (MODIS) radiance-based cloud distance data and the OCO-2 Lite file rawXCO2 for both quality flag =0 (QF0; best quality) and quality flag =1 (QF1; poor quality) data. SHDOM calculations of the ocean and land scenes indicate that the 1D / 3D radiance intensity ratios and rawXCO2 decrease concurrently as the nearest-cloud distance decreases towards zero, especially for the ocean glint QF1 data, which provide the clearest evidence of 3D cloud effects in OCO-2 retrievals. Yearly analysis of OCO-2 O2 A-band continuum radiances indicate that 3D cloud-brightening events are predominant over cloud-shadowing events; therefore, 1D / 3D intensity ratios are predominantly less than unity. Bias corrected (bcXCO2) at cloud distances between 0 and 20 km are calculated for 20∘ latitude bands for 2015–2018. These zonal averages are used to calculate 3D-cloud-effect biases for bcXCO2 data (with a positive bias indicating that OCO-2 underestimates bcXCO2). Averages of 3D-cloud-effect biases, weighted by the number of Lite file data points in each of the nearest-cloud distance bins, in the Northern and Southern hemispheres, are 0.16 (1.31) and 0.26 (1.41) ppm (parts per million), respectively, over the ocean, and −0.13 (0.51) and −0.08 (0.47) ppm over land for QF0 (QF1) data.

Ground-based remote sensing of aerosol properties using high-resolution infrared emission and lidar observations in the High Arctic

Abstract. Arctic amplification, the phenomenon that the Arctic is warming faster than the global mean, is still not fully understood. The Transregional Collaborative Research Centre “TRR 172: ArctiC Amplification: Climate Relevant Atmospheric and SurfaCe Processes, and Feedback Mechanisms (AC)3” program, funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), contributes towards this research topic. For the purpose of measuring aerosol components, a Fourier transform infrared spectrometer (FTIR), for measuring downwelling emission (in operation since 2019), and a Raman lidar are operated at the joint Alfred Wegener Institute for Polar and Marine Research and Paul Emile Victor Institute (AWIPEV) research base in Ny-Ålesund, Spitsbergen (79∘ N, 12∘ E). To carry out aerosol retrieval using measurements from the FTS, the LBLDIS retrieval algorithm, based on a combination of the Line-by-Line Radiative Transfer Model (LBLRTM) and the DIScrete Ordinate Radiative Transfer (DISORT) algorithm, is modified for different aerosol types (dust, sea salt, black carbon, and sulfate), aerosol optical depth (AOD), and effective radius (Reff). Using lidar measurement, an aerosol and cloud classification method is developed to provide basic information about the distribution of aerosols or clouds in the atmosphere and is used as an indicator to perform aerosol or cloud retrievals with the FTS. Therefore, a two-instrument joint-observation scheme is designed and subsequently used on the data measured from 2019 to the present. In order to introduce this measurement technique in detail, an aerosol-only case study is presented using data from 10 June 2020. In the aerosol-only case, the retrieval results show that sulfate is the dominant aerosol throughout the day (τ900cm-1 = 0.007 ± 0.0027), followed by dust (τ900cm-1 = 0.0039 ± 0.0029) and black carbon (τ900cm-1 = 0.0017 ± 0.0007). Sea salt (τ900cm-1 = 0.0012 ± 0.0002), which has the weakest emission ability in the infrared wave band, shows the lowest AOD value. Such proportions of sulfate, dust, and BC also show good agreement with Modern-Era Retrospective analysis for Research and Applications version 2 (MERRA-2) reanalysis data. Additionally, comparison with a Sun photometer (AErosol RObotic NETwork – AERONET) shows the daily variation in the AOD retrieved from FTS to be similar to that retrieved by Sun photometer. Using this method, long-term observations (from April to August 2020) are retrieved and presented. We find that sulfate is often present in the Arctic; it is higher in spring and lower in summer. Similarly, BC is also frequently observed in the Arctic, with less obvious seasonal variation than sulfate. A BC outburst event is observed each spring and summer. In spring, sulfate and BC are dominant, whereas sea salt and dust are relatively low. In addition, a sea salt enhancement event is observed in summertime, which might be due to the melting of sea ice and emissions from nearby open water. From the retrieved results over a long time period, no clear correlations are found; thus, the aforementioned species can be retrieved independently of one another.

Estimation of surface water content at the Tianwen-1 Zhurong landing site

China’s first Mars rover, Zhurong, successfully landed in the south of Utopia Planitia. The surface water content at the landing area can provide constraints on mineral formation conditions and help us better understand the evolution of the Martian aqueous and geological environment. In this work, the surface kinetic temperature of the Zhurong landing area was derived by analyzing data from the Mars Express Observatoire pour la Minéralogie, l’Eau, les Glaces et l’Activité (OMEGA) spectrometer. Using the Discrete Ordinate Radiative Transfer (DISORT) model, we performed atmospheric correction and thermal correction for the OMEGA data to obtain the surface effective single-particle absorption thickness (ESPAT) parameter to evaluate the surface water content. The surface water content distribution at the landing area was relatively uniform at a lateral scale of ~10 km. At the Zhurong landing site, the surface water content in the topmost layer (a few hundred micrometers) of the regolith was 5−8 weight percent water (wt% H₂O), assuming surface particle sizes of <45 μm, or 1.6−2.5 wt% H₂O, assuming surface particle sizes in the range of 125−250 μm. The Mars Surface Composition Detector (MarSCoDe) onboard Zhurong also observed significant H₂O/OH signals in the landing area. Our results provide an important regional context for the hydration state of the area and can be further verified by the H content derived from the Laser-Induced Breakdown Spectrometer (LIBS) data of MarSCoDe.

Scalar thermal radiation using the adding-doubling method.

The scalar radiative transfer equation in the presence of thermal radiation source is solved in detail, using the adding-doubling method; Planck functions within any given layer are assumed to possess constant, linear, or exponential parameterizations with optical thickness. The radiance profile in any zenith direction is calculated directly in terms of matrix inversions. The inputs to the model are the inherent optical properties (layer total single-scattering albedos, scattering phase functions, and optical thickness) along with temperature and altitude profiles, and the top of the atmosphere and ground surface boundary conditions. The algorithm is implemented in a state-of-the-art MATLAB program, with the cosmic microwave background as the source at the upper boundary and a Lambertian surface reflection at the lower boundary. The simulations are validated against the VLIDORT discrete ordinate radiative transfer model. Results are compared in detail for cases with linear and exponential Planck function parameterizations.

Polarized Radiative Transfer Simulations: A Tutorial Review and Upgrades of the Vector Discrete Ordinate Radiative Transfer Computational Tool

We present an overview and several important upgrades to the Vector Discrete Ordinate Radiative Transfer (VDISORT) code. VDISORT is a polarized (vector) radiative transfer code that can be applied to a wide range of research problems including the Earth’s atmosphere and ocean system. First, a solution is developed to the complex algebraic eigenvalue problem resulting when the b2 component of the Stokes scattering matrix is non-zero. This solution is needed to compute the V component of the Stokes vector I=[I∥,I⊥,U,V]T. Second, a significant improvement in computational efficiency is obtained by reducing the dimension of the algebraic eigenvalue by a factor of 2 resulting in a speed increase of about 23 = 8. Third, an important upgrade of the VDISORT code is obtained by developing and implementing a method to enable output at arbitrary polar angles by the integration of the source function (ISF) method for partially reflecting Lambertian as well as general non-Lambertian surfaces. Fourth, a pseudo-spherical treatment has been implemented to provide important corrections for Earth curvature effects at near horizontal solar zenith and observation (viewing) polar angles. Fifth, a post-processing single-scattering correction procedure has been developed to enhance the accuracy and speed for strongly forward-peaked scattering. With these significant improvements the results from the upgraded version of the VDISORT code match published benchmark results for Rayleigh scattering, Mie scattering, and scattering by non-spherical cirrus particles. The performance of VDISORT for a polarized incident beam source is equally satisfactory. The VDISORT vector radiative transfer code is made public and freely available for use by the growing polarimetric research community including the space-borne polarimeters on the future NASA PACE and AOS missions.

Longwave radiative effect of the cloud–aerosol transition zone based on CERES observations

Abstract. This study presents an approach for the quantification of cloud–aerosol transition-zone broadband longwave radiative effects at the top of the atmosphere (TOA) during daytime over the ocean, based on satellite observations and radiative transfer simulation. Specifically, we used several products from MODIS (MODerate Resolution Imaging Spectroradiometer) and CERES (Clouds and the Earth's Radiant Energy System) sensors for the identification and selection of CERES footprints with a horizontally homogeneous transition-zone and clear-sky conditions. For the selected transition-zone footprints, radiative effect was calculated as the difference between the instantaneous CERES TOA upwelling broadband longwave radiance observations and corresponding clear-sky radiance simulations. The clear-sky radiances were simulated using the Santa Barbara DISORT (DIScrete Ordinates Radiative Transfer program for a multi-Layered plane-parallel medium) Atmospheric Radiative Transfer model fed by the hourly ERA5 reanalysis (fifth generation ECMWF ReAnalysis) atmospheric and surface data. The CERES radiance observations corresponding to the clear-sky footprints detected were also used for validating the simulated clear-sky radiances. We tested this approach using the radiative measurements made by the MODIS and CERES instruments on board the Aqua platform over the southeastern Atlantic Ocean during August 2010. For the studied period and domain, transition-zone radiative effect (given in flux units) is on average equal to 8.0 ± 3.7 W m−2 (heating effect; median: 5.4 W m−2), although cases with radiative effects as large as 50 W m−2 were found.

Mapping liquid water content in snow at the millimeter scale: an intercomparison of mixed-phase optical property models using hyperspectral imaging and in situ measurements

Abstract. It is well understood that the distribution and quantity of liquid water in snow is relevant for snow hydrology and avalanche forecasting, yet detecting and quantifying liquid water in snow remains a challenge from the micro- to the macro-scale. Using near-infrared (NIR) spectral reflectance measurements, previous case studies have demonstrated the capability to retrieve surface liquid water content (LWC) of wet snow by leveraging shifts in the complex refractive index between ice and water. However, different models to represent mixed-phase optical properties have been proposed, including (1) internally mixed ice and water spheres, (2) internally mixed water-coated ice spheres, and (3) externally mixed interstitial ice and water spheres. Here, from within a controlled laboratory environment, we determined the optimal mixed-phase optical property model for simulating wet snow reflectance using a combination of NIR hyperspectral imaging, radiative transfer simulations (Discrete Ordinate Radiative Transfer model, DISORT), and an independent dielectric LWC measurement (SLF Snow Sensor). Maps of LWC were produced by finding the lowest residual between measured reflectance and simulated reflectance in spectral libraries, generated for each model with varying LWC and grain size, and assessed against the in situ LWC sensor. Our results show that the externally mixed model performed the best, retrieving LWC with an uncertainty of ∼1 %, while the simultaneously retrieved grain size better represented wet snow relative to the established scaled band area method. Furthermore, the LWC retrieval method was demonstrated in the field by imaging a snowpit sidewall during melt conditions and mapping LWC distribution in unprecedented detail, allowing for visualization of pooling water and flow features.

Characterization of NDSI Variation: Implications for Snow Cover Mapping

The normalized difference snow index (NDSI) plays an important role in mapping snow cover with spaceborne visible and shortwave-infrared imagery. The NDSI variation depends on illuminating-viewing geometry and snow physical properties, including equivalent grain size (EGS), snow depth (SD) and impurity concentration, as well as fractional snow cover (FSC) within a mixed pixel; however, it is still not fully understood. To quantifiably characterize the pattern of snow NDSI variation, we use a light scattering model of snow to calculate bidirectional reflectance and consequent NDSI values for a wide range of illuminating-viewing geometries, SD, and EGS values. In the model designated bicontinuous snow model using Geometric Optics theory and Radiative Transfer Equation (bicontinuous-GO/RTE), snowpack is represented by a bicontinuous microstructure, and bidirectional reflectance is simulated based on geometric optics and vector radiative transfer equation. The discrete ordinates radiative transfer (DISORT) algorithm is used to simulate the soot concentration effect on snow NDSI. A soil spectral reflectance model (SOILSPECT) is utilized with the assumption of the linear spectral mixture of snow and soil to quantify the effect of FSC on NDSI. As for discontinuous forests, an analytical hybrid geometric-optical and radiative transfer (GORT) model in conjunction with the bicontinuous-GO/RTE model and the PROpriétésSPECTrales (PROSPECT) model is used to examine the effect of canopy cover, which is related to the maximal FSC viewable to satellites. Modeling results indicate that: 1) snow NDSI is comparably low at off-nadir viewing angles, and this effect is exacerbated by the decline in solar elevation but limited by large EGS; 2) snow NDSI increases with EGS yet becomes saturated at EGS of 500 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{m}$ </tex-math></inline-formula> ; 3) the effect of SD that is as low as 1 cm on NDSI is rarely noticeable; 4) the concentration of internally mixed soot up to 1 ppm has little reducing effect on snow NDSI (<0.05); 5) the angular effects on the NDSI thresholding method to identify binary snow cover for soil background are nonsignificantly pronounced in the cross plane (CP); 6) NDSI increases linearly with FSC for soil background at nadir as well as in the CP; 7) the SNOw-MAPping algorithm (SNOMAP) method could omit snow cover at large zenith angles for solar zenith angles <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$&gt; 20^{\circ }$ </tex-math></inline-formula> in forests; and 8) forests complicate the nonlinear relationship between NDSI and canopy cover with fully snow-covered ground beneath canopies. These findings imply important uncertainty sources of binary and FSC mapping with NDSI.

Aerosol Characteristics and Their Impact on the Himalayan Energy Budget

The extensive work on the increasing burden of aerosols and resultant climate implications shows a matter of great concern. In this study, we investigate the aerosol optical depth (AOD) variations in the Indian Himalayan Region (IHR) between its plains and alpine regions and the corresponding consequences on the energy balance on the Himalayan glaciers. For this purpose, AOD data from Moderate Resolution Imaging Spectroradiometer (MODIS, MOD-L3), Aerosol Robotic Network (AERONET), India, and Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) were analyzed. Aerosol radiative forcing (ARF) was assessed using the atmospheric radiation transfer model (RTM) integrated into AERONET inversion code based on the Discrete Ordinate Radiative Transfer (DISORT) module. Further, air mass trajectory over the entire IHR was analyzed using a hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) model. We estimated that between 2001 and 2015, the monthly average ARF at the surface (ARFSFC), top of the atmosphere (ARFTOA), and atmosphere (ARFATM) were −89.6 ± 18.6 Wm−2, −25.2 ± 6.8 Wm−2, and +64.4 ± 16.5 Wm−2, respectively. We observed that during dust aerosol transport days, the ARFSFC and TOA changed by −112.2 and −40.7 Wm−2, respectively, compared with low aerosol loading days, thereby accounting for the decrease in the solar radiation by 207% reaching the surface. This substantial decrease in the solar radiation reaching the Earth’s surface increases the heating rate in the atmosphere by 3.1-fold, thereby acting as an additional forcing factor for accelerated melting of the snow and glacier resources of the IHR.

Data-driven acceleration of thermal radiation transfer calculations with the dynamic mode decomposition and a sequential singular value decomposition

We present a method for accelerating discrete ordinates radiative transfer calculations for radiative transfer. Our method works with nonlinear positivity fixes, in contrast to most acceleration schemes. The method is based on the dynamic mode decomposition (DMD) and using a sequence of rank-one updates to compute the singular value decomposition needed for DMD. Using a sequential method allows us to automatically determine the number of solution vectors to include in the DMD acceleration. We present results for slab geometry discrete ordinates calculations with the standard temperature linearization. Compared with positive source iteration, our results demonstrate that our acceleration method reduces the number of transport sweeps required to solve the problem by a factor of about 3 on a standard diffusive Marshak wave problem, a factor of several thousand on a cooling problem where the effective scattering ratio approaches unity, and a factor of 20 improvement in a realistic, multimaterial radiating shock problem.

Uniform convergence of an upwind discontinuous Galerkin method for solving scaled discrete-ordinate radiative transfer equations with isotropic scattering

Uniform convergence of an upwind discontinuous Galerkin method for solving scaled discrete-ordinate radiative transfer equations with isotropic scattering

Radiative transfer acceleration based on the principal component analysis and lookup table of corrections: optimization and application to UV ozone profile retrievals

Abstract. In this work, we apply a principal component analysis (PCA)-based approach combined with lookup tables (LUTs) of corrections to accelerate the Vector Linearized Discrete Ordinate Radiative Transfer (VLIDORT) model used in the retrieval of ozone profiles from backscattered ultraviolet (UV) measurements by the Ozone Monitoring Instrument (OMI). The spectral binning scheme, which determines the accuracy and efficiency of the PCA-RT performance, is thoroughly optimized over the spectral range 265 to 360 nm with the assumption of a Rayleigh-scattering atmosphere above a Lambertian surface. The high level of accuracy (∼ 0.03 %) is achieved from fast-PCA calculations of full radiances. In this approach, computationally expensive full multiple scattering (MS) calculations are limited to a small set of PCA-derived optical states, while fast single scattering and two-stream MS calculations are performed, for every spectral point. The number of calls to the full MS model is only 51 in the application to OMI ozone profile retrievals with the fitting window of 270–330 nm where the RT model should be called at fine intervals (∼ 0.03 nm with ∼ 2000 wavelengths) to simulate OMI measurements (spectral resolution: 0.4–0.6 nm). LUT corrections are implemented to accelerate the online RT model due to the reduction of the number of streams (discrete ordinates) from 8 to 4, while improving the accuracy at the level attainable from simulations using a vector model with 12 streams and 72 layers. Overall, we speed up our OMI retrieval by a factor of 3.3 over the previous version, which has already been significantly sped up over line-by-line calculations due to various RT approximations. Improved treatments for RT approximation errors using LUT corrections improve spectral fitting (2 %–5 %) and hence retrieval errors, especially for tropospheric ozone by up to ∼ 10 %; the remaining errors due to the forward model errors are within 5 % in the troposphere and 3 % in the stratosphere.

Estimation of global horizontal irradiance in China using a deep learning method

ABSTRACT Quasi-real-time estimation of Global Horizontal Irradiance (GHI) is a key parameter for many solar energy applications. We propose the use of a deep belief network (DBN) to estimate GHI under all-sky conditions derived from Himawari-8 satellite images with a high accuracy and high efficiency, and a high spatial and time resolution for a large geographical area. The DBN solver for GHI (DBN-GHI) is based upon a radiative transfer model, Santa Barbara Discrete Ordinate Radiative Transfer (SBDART), to maintain the balance between computational efficiency and accuracy. The computational time of DBN-GHI for one satellite image with more than 400,000 pixels is around 9 seconds. Aerosol was considered as the main attenuation factor for clear skies, while cloud parameters were used for cloudy-sky GHI estimation. The main novelty of this research is that prior to it, there is a dearth of GHI estimations in China at minutely or hourly intervals in all sky conditions. The results of hourly comparison of this with ground-based observations gave a very good Pearson correlation coefficient (r), above 0.95, with a Root-Mean-Square-Error (RMSE) between about 30 to 80 w m−2.

Discrete Ordinate Radiative Transfer Model With the Neural Network Based Eigenvalue Solver: proof Of Concept

Artificial neural networks are attracting increasing attention in various applications. They can be used as ‘universal approximations’, which substitute computationally expensive algorithms by relatively simple sequences of functions, which simulate a reaction of a set of neurons to the incoming signal. In particular, neural networks have proved to be efficient for parameterization of the computationally expensive radiative transfer models (RTMs) in atmospheric remote sensing. Although a direct substitution of RTMs by neural networks can lead to the multiple performance enhancements, such an approach has certain drawbacks, such as loss of generality, robustness issues, etc. In this regard, the neural network is usually trained for a specific application, predefined atmospheric scenarios and a given spectrometer. In this paper a new concept of neural-network based RTMs is examined, in which the neural network substitutes not the whole RTM but rather a part of it (the eigenvalue solver), thereby reducing the computational time while maintaining its generality. The explicit dependencies on geometry of observation and optical thickness of the medium are excluded from training. It is shown that although the speedup factor due to this approach is modest (around 3 times against 103 speed up factor of other approaches reported in recent papers), the resulting neural network is flexible and easy to train. It can be used for arbitrary number of atmospheric layers. Moreover, this approach can be used in conjunction with any RTMs based on the discrete ordinate method. The neural network is applied for simulations of the radiances at the top of the atmosphere in the Huggins band.

Discrete Ordinate Adding Method (DOAM), a new solver for Advanced Radiative transfer Modeling System (ARMS).

Satellite data assimilation requires a computationally fast and accurate radiative transfer model. Currently, three fast models are commonly used in the Numerical Weather Prediction models (NWP) for satellite data assimilation, including Radiative Transfer for TIROS Operational Vertical Sounder (RTTOV), Community Radiative Transfer Model (CRTM), and Advanced Radiative transfer Modeling System (ARMS). ARMS was initiated in 2018 and is now becoming the third pillar supporting many users in NWP and remote sensing fields. Its radiative transfer solvers (e.g. Doubling Adding method) is inherited from CRTM. In this study, we propose a Discrete Ordinate Adding Method (DOAM) to solve the radiative transfer equation including both solar and thermal source terms. In order to accelerate the DOAM computation, the single scattering approximation is used in the layer with an optical depth less than 10-8 or a single scattering albedo less than 10-10. From principles of invariance, the adding method is then applied to link the radiances between the layers. The accuracy of DOAM is evaluated through four benchmark cases. It is shown that the difference between DOAM and DIScrete Ordinate Radiative Transfer (DISORT) decreases with an increase of stream number. The relative bias of the 4-stream DOAM ranges from -5.03 % to 5.92 % in the triple layers of a visible wavelength case, while the maximum bias of the 8-stream DOAM is only about 1 %. The biases can be significantly reduced by the single scattering correction. Comparing to the visible case, the accuracy of the 4-stream DOAM is much higher in the thermal case with a maximum bias -1.69 %. Similar results are also shown in two multiple-layer cases. In the MacBook Pro (15-inch, 2018) laptop, the 2-stream DOAM only takes 1.68 seconds for calculating azimuthally independent radiance of 3000 profiles in the hyper-spectral oxygen A-band (wavelength ranges from 0.757 µm to 0.775 µm), while the 4-stream DOAM takes 4.06 seconds and the 16-stream DOAM takes 45.93 seconds. The time of the 2-, 4- and 16- stream DOAM are 0.86 seconds, 1.09 seconds and 4.34 seconds for calculating azimuthally averaged radiance. DISORT with 16 streams takes 1521.56 seconds and 127.64 seconds under the same condition. As a new solver, DOAM has been integrated into ARMS and is used to simulate the brightness temperatures at MicroWave Humidity Sounder (MWHS) as well as MicroWave Radiation Imager (MWRI) frequencies. The simulations by DOAM are compared to those by Doubling Adding method and accuracy of both solvers shows a general agreement. All the results show that the DOAM is accurate and computational efficient for applications in NWP data assimilation and satellite remote sensing.

Ozone Monitoring Instrument (OMI) Aura nitrogen dioxide standard product version 4.0 with improved surface and cloud treatments

Abstract. We present a new and improved version (V4.0) of the NASA standard nitrogen dioxide (NO2) product from the Ozone Monitoring Instrument (OMI) on the Aura satellite. This version incorporates the most salient improvements for OMI NO2 products suggested by expert users and enhances the NO2 data quality in several ways through improvements to the air mass factors (AMFs) used in the retrieval algorithm. The algorithm is based on the geometry-dependent surface Lambertian equivalent reflectivity (GLER) operational product that is available on an OMI pixel basis. GLER is calculated using the vector linearized discrete ordinate radiative transfer (VLIDORT) model, which uses as input high-resolution bidirectional reflectance distribution function (BRDF) information from NASA's Aqua Moderate Resolution Imaging Spectroradiometer (MODIS) instruments over land and the wind-dependent Cox–Munk wave-facet slope distribution over water, the latter with a contribution from the water-leaving radiance. The GLER combined with consistently retrieved oxygen dimer (O2–O2) absorption-based effective cloud fraction (ECF) and optical centroid pressure (OCP) provide improved information to the new NO2 AMF calculations. The new AMFs increase the retrieved tropospheric NO2 by up to 50 % in highly polluted areas; these differences arise from both cloud and surface BRDF effects as well as biases between the new MODIS-based and previously used OMI-based climatological surface reflectance data sets. We quantitatively evaluate the new NO2 product using independent observations from ground-based and airborne instruments. The new V4.0 data and relevant explanatory documentation are publicly available from the NASA Goddard Earth Sciences Data and Information Services Center (https://disc.gsfc.nasa.gov/datasets/OMNO2_V003/summary/, last access: 8 November 2020), and we encourage their use over previous versions of OMI NO2 products.

Satellite-based radiative forcing by light-absorbing particles in snow across the Northern Hemisphere

Abstract. Snow is the most reflective natural surface on Earth and consequently plays an important role in Earth's climate. Light-absorbing particles (LAPs) deposited on the snow surface can effectively decrease snow albedo, resulting in positive radiative forcing. In this study, we used remote-sensing data from NASA's Moderate Resolution Imaging Spectroradiometer (MODIS) and the Snow, Ice, and Aerosol Radiative (SNICAR) model to quantify the reduction in snow albedo due to LAPs before validating and correcting the data against in situ observations. We then incorporated these corrected albedo-reduction data in the Santa Barbara DISORT (Discrete Ordinate Radiative Transfer) Atmospheric Radiative Transfer (SBDART) model to estimate Northern Hemisphere radiative forcing except for midlatitude mountains in December–May for the period 2003–2018. Our analysis reveals an average corrected reduction in snow albedo (ΔαMODIS,correctedLAPs) of ∼ 0.021 under all-sky conditions, with daily radiative forcing (RFMODIS,dailyLAPs) values of ∼ 2.9 W m−2, over land areas with complete or near-complete snow cover and with little or no vegetation above the snow in the Northern Hemisphere. We also observed significant spatial variations in ΔαMODIS,correctedLAPs and RFMODIS,dailyLAPs, with the lowest respective values (∼ 0.016 and ∼ 2.6 W m−2) occurring in the Arctic and the highest (∼ 0.11 and ∼ 12 W m−2) in northeastern China. From MODIS retrievals, we determined that the LAP content of snow accounts for 84 % and 70 % of the spatial variability in albedo reduction and radiative forcing, respectively. We also compared retrieved radiative forcing values with those of earlier studies, including local-scale observations, remote-sensing retrievals, and model-based estimates. Ultimately, estimates of radiative forcing based on satellite-retrieved data are shown to represent true conditions on both regional and global scales.