Two-stream Radiative Transfer Research Articles

Linking lidar multiple scattering profiles to snow depth and snow density: an analytical radiative transfer analysis and the implications for remote sensing of snow

Lidar multiple scattering measurements provide the probability distribution of the distance laser light travels inside snow. Based on an analytic two-stream radiative transfer solution, the present study demonstrates why/how these lidar measurements can be used to derive snow depth and snow density. In particular, for a laser wavelength with little snow absorption, an analytical radiative transfer solution is leveraged to prove that the physical snow depth is half of the average distance photons travel inside snow and that the relationship linking lidar measurements and the extinction coefficient of the snow is valid. Theoretical formulas that link lidar measurements to the extinction coefficient and the effective grain size of snow are provided. Snow density can also be derived from the multi-wavelength lidar measurements of the snow extinction coefficient and snow effective grain size. Alternatively, lidars can provide the most direct snow density measurements and the effective discrimination between snow and trees by adding vibrational Raman scattering channels.

Impact of the sampling procedure on the specific surface area of snow measurements with the IceCube

Abstract. The specific surface area (SSA) of snow can be directly measured by X-ray computed tomography or indirectly measured using the reflectance of near-infrared light. The IceCube (IC) is a well-established spectroscopic instrument that uses a near-infrared wavelength of 1310 nm. We compared the SSA of six snow types measured with both instruments. We measured significantly higher values with the IC, with a relative percentage difference of between 20 % and 52 % for snow types with an SSA between 5 and 25 m2 kg−1. We found no significant difference for snow with an SSA between 30 and 80 m2 kg−1. The difference is statistically significant between snow types but not uniquely related to the SSA. We suspected that particles artificially created during the sample preparation were the source of the difference. We sampled, measured and counted these particles to conduct numerical simulations with the TwostreAm Radiative TransfEr in Snow (TARTES) radiation transfer solver. The results support the hypothesis that these small, artificial particles can significantly increase the reflectivity at 1310 nm and, therefore, lead to an overestimation of the SSA.

Monte Carlo radiative transfer with explicit absorption to simulate absorption, scattering, and stimulated emission

Context. The Monte Carlo method is probably the most widely used approach to solve the radiative transfer problem, especially in a general 3D geometry. The physical processes of emission, absorption, and scattering are easily incorporated in the Monte Carlo framework. Net stimulated emission, or absorption with a negative cross section, does not fit this method, however.Aims. We explore alterations to the standard photon packet life cycle in Monte Carlo radiative transfer that allow the treatment of net stimulated emission without loss of generality or efficiency.Methods. We present the explicit absorption technique that allows net stimulated emission to be handled efficiently. It uses the scattering rather than the extinction optical depth along a photon packet’s path to randomly select the next interaction location, and offers a separate, deterministic treatment of absorption. We implemented the technique in a special-purpose Monte Carlo code for a two-stream 1D radiative transfer problem and in the fully featured 3D code SKIRT, and we studied its overall performance using quantitative statistical tests.Results. Our special-purpose code is capable of recovering the analytical solutions to the two-stream problem in all regimes, including the one of strong net stimulated emission. The implementation in SKIRT is straightforward, as the explicit absorption technique easily combines with the variance reduction and acceleration techniques already incorporated. In general, explicit absorption tends to improve the efficiency of the Monte Carlo routine in the regime of net absorption.Conclusions. Explicit absorption allows the treatment of net stimulated emission in Monte Carlo radiative transfer, it interfaces smoothly with other variance reduction and acceleration techniques, and it tends to improve the efficiency of the simulations in the net absorption regime. We recommend to always include this new technique in Monte Carlo radiative transfer.

The THOR + HELIOS general circulation model: multiwavelength radiative transfer with accurate scattering by clouds/hazes

ABSTRACT General circulation models (GCMs) provide context for interpreting multiwavelength, multiphase data of the atmospheres of tidally locked exoplanets. In the current study, the non-hydrostatic THOR GCM is coupled with the HELIOS radiative transfer solver for the first time, supported by an equilibrium chemistry solver (FastChem), opacity calculator (HELIOS-K), and Mie scattering code (LX-MIE). To accurately treat the scattering of radiation by medium-sized to large aerosols/condensates, improved two-stream radiative transfer is implemented within a GCM for the first time. Multiple scattering is implemented using a Thomas algorithm formulation of the two-stream flux solutions, which decreases the computational time by about 2 orders of magnitude compared to the iterative method used in past versions of HELIOS. As a case study, we present four GCMs of the hot Jupiter WASP-43b, where we compare the temperature, velocity, entropy, and streamfunction, as well as the synthetic spectra and phase curves, of runs using regular versus improved two-stream radiative transfer and isothermal versus non-isothermal layers. While the global climate is qualitatively robust, the synthetic spectra and phase curves are sensitive to these details. A THOR + HELIOS WASP-43b GCM (horizontal resolution of about 4 deg on the sphere and with 40 radial points) with multiwavelength radiative transfer (30 k-table bins) running for 3000 Earth days (864 000 time-steps) takes about 19–26 d to complete depending on the type of GPU.

Satellite retrieval of benthic reflectance by combining lidar and passive high-resolution imagery: Case-I water

Under the background of global change, increasing attention has been paid to the changes of benthic habitats in shallow ocean ecosystems (e.g., seagrass beds and coral reefs). Optical satellite remote sensing via both active and passive methods plays an important role in monitoring the health of benthic habitats by retrieving benthic reflectance spectra, but it remains difficult to accurately retrieve benthic reflectance spectra from only active or passive remote sensing because of the coupling between water column scattering and benthic reflectance. Here, we developed a semi-analytical model to retrieve benthic reflectance spectra in Case-I waters by combining active lidar and passive high-resolution imagery. Based on two-stream radiative transfer theory, the analytical relationship among the remote sensing reflectance (Rrs) and water column reflectance (Rw), benthic reflectance (Rb), diffuse attenuation coefficient (Kd), and water depth was established. The lidar data at a certain wavelength were applied to derive the water depth and the chlorophyll concentration (chl) along the lidar track. Then, the values of Kd at different wavelengths were estimated from the derived chl. In addition, we established a look-up-table (LUT) for the relationship between Rw and chl and water depth using Hydrolight simulation, and the Rw values at different wavelengths were then estimated by the lidar-derived chl and water depth. Finally, Rb(λ) values at different wavelengths along the lidar track were retrieved from the Rrs(λ) values observed by passive high-resolution imagery and the values of Rw(λ), Kd(λ), and water depth derived by lidar observation. The accuracy of the model was verified by using the Hydrolight simulated datasets, and the high correlation coefficient (R) revealed promising model performance for different benthic habitats, e.g., R > 0.9 for typical clean shallow water (chl = 0.5 mg/m3, H < 4 m) for the wavelength range of 400–640 nm. The model was further applied to real satellite data from ICESat-2 lidar and passive high-resolution satellite imagery (multispectral imagery of Sentinel-2 and hyperspectral imagery of Zhuhai−1) at two different benthic habitat sites (seagrass beds in Xincun Bay and coral reefs in the Huaguang Reef) in the South China Sea, and the results revealed that the model could reproduce the benthic spectra in both magnitude and shape. Overall, the proposed model can reliably yield benthic reflectance spectra along the lidar track without any requirement on prior knowledge, which should be beneficial for further benthic habitat health monitoring.

Jet streams and tracer mixing in the atmospheres of brown dwarfs and isolated young giant planets

ABSTRACT Observations of brown dwarfs and relatively isolated young extrasolar giant planets have provided unprecedented details to probe atmospheric dynamics in a new regime. Questions about mechanisms governing the global circulation and its fundamental nature remain to be completely addressed. Previous studies have shown that small-scale randomly varying thermal perturbations resulting from interactions between convection and the overlying stratified layers can drive zonal jet streams, waves, and turbulence. In this work, we improve upon our previous work by using a general circulation model coupled with a two-stream grey radiative transfer scheme to represent more realistic heating and cooling rates. We examine the formation of zonal jets and their time evolution, and vertical mixing of passive tracers including clouds and chemical species. Under relatively weak radiative and frictional dissipation, robust zonal jets with speeds up to a few hundred m s−1 are typical outcomes. The off-equatorial jets tend to be pressure independent, while the equatorial jets exhibit significant vertical wind shear. On the other hand, models with strong dissipation inhibit the jet formation and leave isotropic turbulence in off-equatorial regions. Quasi-periodic oscillations of the equatorial flow with periods ranging from tens of days to months are prevalent at relatively low atmospheric temperatures. Submicron cloud particles can be easily transported to several scale heights above the condensation level, while larger particles form thinner layers. Cloud decks are significantly inhomogeneous near their cloud tops. Chemical tracers with chemical time-scales &amp;gt;105 s can be driven out of equilibrium. The equivalent vertical diffusion coefficients, Kzz, for the global-mean tracer transport are diagnosed from our models and are typically on the order of 1–102 m2 s−1. Finally, we derive an analytic estimation of Kzz for different types of tracers under relevant conditions.

Modeling the High-resolution Emission Spectra of Clear and Cloudy Nontransiting Hot Jupiters

Abstract The advent of high-resolution spectroscopy (R ≳ 25,000) as a method for characterization of exoplanet atmospheres has expanded our capability to study nontransiting planets, vastly increasing the number of planets accessible for observation. Many of the most favorable targets for atmospheric characterization are hot Jupiters, where we expect large spatial variation in physical conditions such as temperature, wind speed, and cloud coverage, making viewing geometry important. Three-dimensional models have generally simulated observational properties of hot Jupiters assuming edge-on viewing, which can be compared to observations of transiting planets, but neglected the large fraction of planets without nearly edge-on orbits. As the first investigation of how orbital inclination manifests in high-resolution emission spectra from three-dimensional models, we use a general circulation model to simulate the atmospheric structure of Upsilon Andromedae b, a typical nontransiting hot Jupiter with high observational interest, due the brightness of its host star. We compare models with and without clouds, and find that cloud coverage intensifies spatial variations by making colder regions dimmer and relatedly enhancing emission from the clear, hotter regions. This increases both the net Doppler shifts and the variation of the continuum flux amplitude over the course of the planet’s orbit. In order to accurately capture scattering from clouds, we implement a generalized two-stream radiative transfer routine for inhomogeneous multiple scattering atmospheres. As orbital inclination decreases, four key features of the high-resolution emission spectra also decrease in both the clear and cloudy models: (1) the average continuum flux level, (2) the amplitude of the variation in continuum with orbital phase, (3) net Doppler shifts of spectral lines, and (4) Doppler broadening in the spectra. Models capable of treating inhomogeneous cloud coverage and different viewing geometries are critical in understanding results from high-resolution emission spectra, enabling an additional avenue to investigate these extreme atmospheres.

A versatile method for computing optimized snow albedo from spectrally fixed radiative variables: VALHALLA v1.0

Abstract. In climate models, the snow albedo scheme generally calculates only a narrowband or broadband albedo, which leads to significant uncertainties. Here, we present the Versatile ALbedo calculation metHod based on spectrALLy fixed radiative vAriables (VALHALLA version 1.0) to optimize spectral snow albedo calculation. For this optimization, the energy absorbed by the snowpack is calculated by the spectral albedo model Two-streAm Radiative TransfEr in Snow (TARTES) and the spectral irradiance model Santa Barbara DISORT Atmospheric Radiative Transfer (SBDART). This calculation takes into account the spectral characteristics of the incident radiation and the optical properties of the snow based on an analytical approximation of the radiative transfer of snow. For this method, 30 wavelengths, called tie points (TPs), and 16 reference irradiance profiles are calculated to incorporate the absorbed energy and the reference irradiance. The absorbed energy is then interpolated for each wavelength between two TPs with adequate kernel functions derived from radiative transfer theory for snow and the atmosphere. We show that the accuracy of the absorbed energy calculation primarily depends on the adaptation of the irradiance of the reference profile to that of the simulation (absolute difference &lt;1 W m−2 for broadband absorbed energy and absolute difference &lt;0.005 for broadband albedo). In addition to the performance in terms of accuracy and calculation time, the method is adaptable to any atmospheric input (broadband, narrowband) and is easily adaptable for integration into a radiative scheme of a global or regional climate model.

Retrievals of Arctic sea ice melt pond depth and underlying ice thickness using optical data

Melt pond is a distinctive characteristic of the summer Arctic, which affects energy balance in the Arctic system. The Delta-Eddington model (BL) and Two-strEam rAdiative transfer model (TEA) are employed to retrieving pond depth Hp and underlying ice thickness H i according to the ratio X of the melt-pond albedo in two bands. Results showed that when λ1 = 359 nm and λ2 = 605 nm, the Pearson’s correlation coefficient r between X and Hp is 0.99 for the BL model. The result of TEA model was similar to the BL model. The retrievals of Hp for the two models agreed well with field observations. For H i, the highest r (0.99) was obtained when λ 1 = 447 nm and λ2 = 470 nm for the BL model, λ 1 = 447 nm and λ 2 = 451 nm for the TEA model. Furthermore, the BL model was more suitable for the retrieval of thick ice (0 Citation :Zhang H, Yu M, Lu P, et al. Retrievals of Arctic sea ice melt pond depth and underlying ice thickness using optical data. Adv Polar Sci, 2021, 32(2): 105-117, doi: 10.13679/j.advps.2021.0021

Inverse Modeling of Radiative Transfer by Two-Stream Approximation using the Luus-Jaakola Method

The simulation of terrestrial ecosystem processes, using numerical biosphere-atmosphere models that can be coupled to the Atmospheric Models, assist in a better diagnosis and forecast of climate and weather. To be able to represent a particular region, biome or ecosystem, the model parameters need to be adjusted for local conditions. This work aims to assess the Luus-Jaakola (LJ) method in the optimization of the parameters in a two-stream radiative transfer model applied to a vegetation canopy. Solar radiation components (incident, S↓, and reflected, S↑) were measured above a sugarcane crop in a Tropical region from February 17 to 24, 2006. Among the combinations of internal and external iterations evaluated for Luss-Jaakola method, 60/30 (external/internal) iterations presented more precise albedo (∝ = S↑/S↓) simulated (r^2 = 0.7386) and, for the accuracy of the simulated ∝, even though the 60/40 combination had the smallest percentual error (6.40%), the 60/30 combination was 0.03% higher. The precision and accuracy of S↑ was greater with the parameters obtained by the inverse problem with the combination of 60/30 (external/internal) iterations respectively. In general, the behavior of simulated S↑ at the top of the canopy was underestimated compared to the observed S↑, especially in the early morning. For the simulated ∝ at the top of the canopy, the model's overestimation was observed at the lowest values of albedo. When the largest albedos are observed, only at the beginning of the day the model underestimated the values. As shown by the tests result, the parameters optimized by Luus-Jaakola method have an adequate representation of the observed data.

Bi-hemispherical Canopy Reflectance Model with Surface Heterogeneity Effects for the Estimation of LAI and fAPAR from MODIS White-Sky Spectral Albedo Data

Bi-hemispherical reflectance (BHR), in the land surface research community also known as “white-sky albedo”, is independent of the directions of incidence and viewing. For vegetation canopies, it is also nearly independent of the leaf angle distribution, and therefore it can be considered an optical quantity that is only dependent on material properties. For the combination leaf canopy and soil background, the most influential material properties are the canopy LAI (leaf area index), optical properties of the leaves, and soil brightness. When the leaf and soil optical properties are known or assumed, one may estimate the canopy LAI from its white-sky spectral albedo. This is also because a simple two-stream radiative transfer (RT) model is available for the BHR of the leaf canopy and soil combination. In this contribution, crown clumping and lateral linear mixing effects are incorporated in this model. A new procedure to estimate soil brightness is introduced here, even under a moderate layer of green vegetation. The procedure uses the red and NIR spectral bands. A MODIS white-sky albedo product at a spatial resolution of 0.05° is used as a sample input to derive global maps of LAI, soil brightness, and fAPAR at the local moments of minimum and maximum NDVI over a 20-year period. These maps show a high degree of spatial coherence and demonstrate the possible utility of products that can be generated with little effort by using a direct LUT technique.

Cutting out the middleman: calibrating and validating a dynamic vegetation model (ED2-PROSPECT5) using remotely sensed surface reflectance

Abstract. Canopy radiative transfer is the primary mechanism by which models relate vegetation composition and state to the surface energy balance, which is important to light- and temperature-sensitive plant processes as well as understanding land–atmosphere feedbacks. In addition, certain parameters (e.g., specific leaf area, SLA) that have an outsized influence on vegetation model behavior can be constrained by observations of shortwave reflectance, thus reducing model predictive uncertainty. Importantly, calibrating against radiative transfer outputs allows models to directly use remote sensing reflectance products without relying on highly derived products (such as MODIS leaf area index) whose assumptions may be incompatible with the target vegetation model and whose uncertainties are usually not well quantified. Here, we created the EDR model by coupling the two-stream representation of canopy radiative transfer in the Ecosystem Demography model version 2 (ED2) with a leaf radiative transfer model (PROSPECT-5) and a simple soil reflectance model to predict full-range, high-spectral-resolution surface reflectance that is dependent on the underlying ED2 model state. We then calibrated this model against estimates of hemispherical reflectance (corrected for directional effects) from the NASA Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) and survey data from 54 temperate forest plots in the northeastern United States. The calibration significantly reduced uncertainty in model parameters related to leaf biochemistry and morphology and canopy structure for five plant functional types. Using a single common set of parameters across all sites, the calibrated model was able to accurately reproduce surface reflectance for sites with highly varied forest composition and structure. However, the calibrated model's predictions of leaf area index (LAI) were less robust, capturing only 46 % of the variability in the observations. Comparing the ED2 radiative transfer model with another two-stream soil–leaf–canopy radiative transfer model commonly used in remote sensing studies (PRO4SAIL) illustrated structural errors in the ED2 representation of direct radiation backscatter that resulted in systematic underestimation of reflectance. In addition, we also highlight that, to directly compare with a two-stream radiative transfer model like EDR, we had to perform an additional processing step to convert the directional reflectance estimates of AVIRIS to hemispherical reflectance (also known as “albedo”). In future work, we recommend that vegetation models add the capability to predict directional reflectance, to allow them to more directly assimilate a wide range of airborne and satellite reflectance products. We ultimately conclude that despite these challenges, using dynamic vegetation models to predict surface reflectance is a promising avenue for model calibration and validation using remote sensing data.

Accuracy Enhancement of the Two-Stream Radiative Transfer Model for Computing Absorption Bands at the Presence of Aerosols

The two-stream model is the fastest radiative transfer model among those based on the discrete ordinate method. Although its accuracy is not high enough to be used in applications, the two-stream model gets more attention in computationally demanding tasks such as line-by-line simulations in the gaseous absorption bands. For this reason, we designed the cluster low-streams regression (CLSR) technique, in which a spectrum computed with a two-stream model, is refined by using statistical dependencies between two- and multistream radiative transfer models. In this paper, we examine the efficiency of this approach for computing Hartley-Huggins, O2 A-, water vapour and CO2 bands at the presence of aerosols. The numerical results evidence that the errors of the CLSR method is not biased and around 0.05 %, while the performance enhancement is two orders of magnitude.

Effect of small-scale snow surface roughness on snow albedo and reflectance

Abstract. The primary goal of this paper is to present a model of snow surface albedo accounting for small-scale surface roughness effects. The model is based on photon recollision probability, and it can be combined with existing bulk volume albedo models, such as Two-streAm Radiative TransfEr in Snow (TARTES). The model is fed with in situ measurements of surface roughness from plate profile and laser scanner data, and it is evaluated by comparing the computed albedos with observations. It provides closer results to empirical values than volume-scattering-based albedo simulations alone. The impact of surface roughness on albedo increases with the progress of the melting season and is larger for larger solar zenith angles. In absolute terms, small-scale surface roughness can decrease the total albedo by up to about 0.1. As regards the bidirectional reflectance factor (BRF), it is found that surface roughness increases backward scattering especially for large solar zenith angle values.

Evaluation of a new snow albedo scheme for the Greenland ice sheet in the Regional Atmospheric Climate Model (RACMO2)

Abstract. Snow and ice albedo schemes in present-day climate models often lack a sophisticated radiation penetration scheme and do not explicitly include spectral albedo variations. In this study, we evaluate a new snow albedo scheme in the Regional Atmospheric Climate Model (RACMO2) for the Greenland ice sheet, version 2.3p3, that includes these processes. The new albedo scheme uses the Two-streAm Radiative TransfEr in Snow (TARTES) model and the Spectral-to-NarrOWBand ALbedo (SNOWBAL) module, version 1.2. Additionally, the bare-ice albedo parameterization has been updated. The snow and ice broadband and narrowband albedo output of the updated version of RACMO2 is evaluated using the Programme for Monitoring of the Greenland Ice Sheet (PROMICE) and Kangerlussuaq transect (K-transect) in situ data and Moderate Resolution Imaging Spectroradiometer (MODIS) remote-sensing observations. Generally, the modeled narrowband and broadband albedo is in very good agreement with satellite observations, leading to a negligible domain-averaged broadband albedo bias for the interior. Some discrepancies are, however, observed close to the ice margin. Compared to the previous model version, RACMO2.3p2, the broadband albedo is considerably higher in the bare-ice zone during the ablation season, as atmospheric conditions now alter the bare-ice broadband albedo. For most other regions, however, the updated broadband albedo is lower due to spectral effects, radiation penetration or enhanced snow metamorphism.

Can the Aerosol Absorption Ångström Exponent Represent Aerosol Color in the Atmosphere: A Numerical Study

The aerosol absorption Ångström exponent (AAE) is widely used to indicate aerosol absorption spectrum variations and is an important parameter for characterizing aerosol optical absorption properties. This study discusses the relationship between aerosol AAEs and their colors numerically. By combining light scattering simulations, a two-stream radiative transfer model, and an RGB (Red, Green, and Blue) color model, aerosol colors that can be sensed by human eyes are numerically generated with both the solar spectrum and human eye response taken into account. Our results indicate that the responses of human eyes to visible light might be more significant than the incident spectrum in the simulation of aerosol color in the atmosphere. Using the improved numerical simulation algorithm, we obtain the color change of absorption aerosols with different AAEs. When the AAE value is small, the color of the aerosol is generally black and gray. When the AAE value increases to approximately 2 and the difference between the light transmittances at wavelengths of 400 nm and 730 nm is greater than 0.2, the aerosol will appear brown or yellow.

A module to convert spectral to narrowband snow albedo for use in climate models: SNOWBAL v1.2

Abstract. Snow albedo schemes in regional climate models often lack a sophisticated radiation penetration scheme and generally compute only a broadband albedo. Here, we present the Spectral-to-NarrOWBand ALbedo module (SNOWBAL, version 1.2) to couple effectively a spectral albedo model with a narrowband radiation scheme. Specifically, the Two-streAm Radiative TransfEr in Snow model (TARTES) is coupled with the European Centre for Medium-Range Weather Forecasts (ECMWF) Integrated Forecast System (IFS), cycle 33R1, atmospheric radiation scheme based on the Rapid Radiation Transfer Model, which is embedded in the Regional Atmospheric Climate Model version 2.3p2 (RACMO2). This coupling allows to explicitly account for the effect of clouds, water vapor, snow impurities and snow metamorphism on albedo. Firstly, we present a narrowband albedo method to project the spectral albedos of TARTES onto the 14 spectral bands of the IFS shortwave radiation scheme using a representative wavelength (RW) for each band. Using TARTES and spectral downwelling surface irradiance derived with the DIScrete Ordinate Radiative Transfer atmospheric model, we show that RWs primarily depend on the solar zenith angle (SZA), cloud content and water vapor. Secondly, we compare the TARTES narrowband albedo, using offline RACMO2 results for south Greenland, with the broadband albedo parameterizations of Gardner and Sharp (2010), currently implemented in RACMO2, and the multi-layered parameterization of Kuipers Munneke et al. (2011, PKM). The actual absence of radiation penetration in RACMO2 leads on average to a higher albedo compared with TARTES narrowband albedo. Furthermore, large differences between the TARTES narrowband albedo and PKM and RACMO2 are observed for high SZA and clear-sky conditions, and after melt events when the snowpack is very inhomogeneous. This highlights the importance of accounting for spectral albedo and radiation penetration to simulate the energy budget of the Greenland ice sheet.

Intercomparison and improvement of two-stream shortwave radiative transfer schemes in Earth system models for a unified treatment of cryospheric surfaces

Abstract. Snow is an important climate regulator because it greatly increases the surface albedo of middle and high latitudes of the Earth. Earth system models (ESMs) often adopt two-stream approximations with different radiative transfer techniques, the same snow therefore has different solar radiative properties depending whether it is on land or on sea ice. Here we intercompare three two-stream algorithms widely used in snow models, improve their predictions at large zenith angles, and introduce a hybrid model suitable for all cryospheric surfaces in ESMs. The algorithms are those employed by the SNow ICe and Aerosol Radiative (SNICAR) module used in land models, dEdd–AD used in Icepack, the column physics used in the Los Alamos sea ice model CICE and MPAS-Seaice, and a two-stream discrete-ordinate (2SD) model. Compared with a 16-stream benchmark model, the errors in snow visible albedo for a direct-incident beam from all three two-stream models are small (&lt;±0.005) and increase as snow shallows, especially for aged snow. The errors in direct near-infrared (near-IR) albedo are small (&lt;±0.005) for solar zenith angles θ&lt;75∘, and increase as θ increases. For diffuse incidence under cloudy skies, dEdd–AD produces the most accurate snow albedo for both visible and near-IR (&lt;±0.0002) with the lowest underestimate (−0.01) for melting thin snow. SNICAR performs similarly to dEdd–AD for visible albedos, with a slightly larger underestimate (−0.02), while it overestimates the near-IR albedo by an order of magnitude more (up to 0.04). 2SD overestimates both visible and near-IR albedo by up to 0.03. We develop a new parameterization that adjusts the underestimated direct near-IR albedo and overestimated direct near-IR heating persistent across all two-stream models for θ&gt;75∘. These results are incorporated in a hybrid model SNICAR-AD, which can now serve as a unified solar radiative transfer model for snow in ESM land, land ice, and sea ice components.

Documentation of the NASA/Ames Legacy Mars Global Climate Model: Simulations of the present seasonal water cycle

We describe and document the physics packages in the legacy NASA/Ames Mars Global Climate Model, present simulations of the seasonal water cycle and how it compares with observations, assess the role of radiatively active clouds on the water cycle and planetary eddies, and discuss the strengths and weakness of the model and the implication for future efforts. The physics packages we describe include the treatment of surface properties, the ground temperature model, planetary boundary layer scheme, sublimation physics, cloud microphysics, the use of a moment method for tracer transport, a semi-interactive dust tracking scheme, and a two-stream radiative transfer code based on correlated-k's. With virtually no tuning of the water cycle and assuming the north polar residual water ice cap is the only source of water we find the model gives a reasonably good simulation of the present seasonal water cycle. No persistent clouds form over the residual cap, seasonal variations in column vapor abundances are similar to those observed, the aphelion cloud belt has about the right opacity, and surface and air temperatures are in reasonably good agreement with observations. The radiative effect of clouds does not significantly alter the seasonal and spatial variation of the moisture fields, though the clouds are thicker and the atmosphere somewhat wetter. As others have found cloud radiative forcing amplifies the mean meridional circulation, transient baroclinic eddies, and global thermal tides. However, it also changes the characteristics of forced stationary waves in ways that are not straightforward to understand. The main weakness of the model, we believe, is sluggish vertical mixing. Water is not transported high enough in the model and as a consequence the water cycle is too dry, the aphelion cloud belt is too low, and the mean meridional circulation is too shallow. These, we feel, could be remedied by some combination of non-local mixing, deep mountain-induced circulations, better horizontal and vertical resolution, and/or gravity wave drag. Efforts are now underway to study these issues as we are transitioning away from our legacy code to one with a more modern dynamical core.

Analytical Models of Exoplanetary Atmospheres. VI. Full Solutions for Improved Two-stream Radiative Transfer, Including Direct Stellar Beam

Abstract Two-stream radiative transfer is used frequently in Earth, planetary, and exoplanetary sciences due to its simplicity and ease of implementation. However, a longstanding limitation of the two-stream approximation is its inaccuracy in the presence of medium-sized or large aerosols. This limitation was lifted by the discovery of the improved two-stream technique, where the accuracy of the scattering greenhouse effect is matched to that of multi-stream calculations by construction. In this study, we derive the full solutions for improved two-stream radiative transfer, following its introduction by Heng &amp; Kitzmann, and include contributions from the direct stellar beam. The generalization of the original two-stream flux solutions comes in the form of a correction factor, traditionally set to unity, which is the ratio of a pair of first Eddington coefficients. We derive an analytical expression for this correction factor and also provide a simple fitting function for its ease of use by other workers. We prove that the direct stellar beam is associated with a second Eddington coefficient that is on the order of unity. Setting this second Eddington coefficient to 2/3 and reproduces the Eddington and quadrature closures, respectively, associated with the direct beam. We use our improved two-stream solutions for the fluxes to derive two-stream source function solutions for both the intensity and fluxes.