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At least 1,423 records · Page 79

Re-Evaluation of Low Cloud Amount Relationships With Lower-Tropospheric Stability and Estimated Inversion Strength

Lower-tropospheric stability (LTS) and estimated inversion strength (EIS) have a widely accepted relationship with low cloud amount and are key observational foundations for understanding and modeling low-level stratiform clouds. Using the updated surface-based and satellite cloud data, we find that low cloud amount is not as strongly correlated with LTS, and not as sensitive to LTS, as established in the past. EIS does not provide a stronger correlation with low cloud amount than LTS over all eight regions (including the midlatitudes). Further analyzing the relationships between LTS and EIS with different types of low clouds, we find that there is a strong correlation of LTS and EIS with stratocumulus only. This explains the weaker correlation of low cloud fraction (including cumulus, stratocumulus, and stratus) to both LTS and EIS. These results also suggest the need to re-evaluate these relationships in Earth system models. Plain Language Summary: Low-level clouds play an important role in the global radiation budget. Low cloud amount has two established linear relationships with lower-tropospheric stability (LTS) and estimated inversion strength (ETS). These two relationships are re-evaluated here using three separate observational cloud and two reanalysis datasets for three distinct but overlapping time periods. The analysis shows that the strength of the LTS and ETS relationships with low cloud amount varies, depending on the cloud data used. They have a strong relationship with stratocumulus cloud amount only.

Lauren Cutler↗

Key drivers of cloud response to surface-active organics

Aerosol-cloud interactions constitute the largest source of uncertainty in global radiative forcing estimates, hampering our understanding of climate evolution. Recent empirical evidence suggests surface tension depression by organic aerosol to significantly influence the formation of cloud droplets, and hence cloud optical properties. In climate models, however, surface tension of water is generally assumed when predicting cloud droplet concentrations. Here we show that the sensitivity of cloud microphysics, optical properties and shortwave radiative effects to the surface phase are dictated by an interplay between the aerosol particle size distribution, composition, water availability and atmospheric dynamics. We demonstrate that accounting for the surface phase becomes essential in clean environments in which ultrafine particle sources are present. Through detailed sensitivity analysis, quantitative constraints on the key drivers – aerosol particle number concentrations, organic fraction and fixed updraft velocity – are derived for instances of significant cloud microphysical susceptibilities to the surface phase.

54 ENVIRONMENTAL SCIENCES↗

The Role of Clouds: An Introduction and Rapporteur Report

This paper presents an overview of discussions during the Cloud s Role session at the Observing and Modelling Earth s Energy Flows Workshop. N. Loeb and B. Soden convened this session including 10 presentations by B. Stevens, B. Wielicki, G. Stephens, A. Clement, K. Sassen, D. Hartmann, T. Andrews, A. Del Genio, H. Barker, and M. Sugi addressing critical aspects of the role of clouds in modulating Earth energy flows. Presentation topics covered a diverse range of areas from cloud microphysics and dynamics, cloud radiative transfer, and the role of clouds in large-scale atmospheric circulations patterns in both observations and atmospheric models. The presentations and discussions, summarized below, are organized around several key questions raised during the session. (1) What is the best way to evaluate clouds in climate models? (2) How well do models need to represent clouds to be acceptable for making climate predictions? (3) What are the largest uncertainties in clouds? (4) How can these uncertainties be reduced? (5) What new observations are needed to address these problems? Answers to these critical questions are the topics of ongoing research and will guide the future direction of this area of research.

Taylor, Patrick C.↗

Classification of Clouds and Deep Convection from GEOS-5 Using Satellite Observations

With the increased resolution of global atmospheric models and the push toward global cloud resolving models, the resemblance of model output to satellite observations has become strikingly similar. As we progress with our adaptation of the Goddard Earth Observing System Model, Version 5 (GEOS-5) as a high resolution cloud system resolving model, evaluation of cloud properties and deep convection require in-depth analysis beyond a visual comparison. Outgoing long-wave radiation (OLR) provides a sufficient comparison with infrared (IR) satellite imagery to isolate areas of deep convection. We have adopted a binning technique to generate a series of histograms for OLR which classify the presence and fraction of clear sky versus deep convection in the tropics that can be compared with a similar analyses of IR imagery from composite Geostationary Operational Environmental Satellite (GOES) observations. We will present initial results that have been used to evaluate the amount of deep convective parameterization required within the model as we move toward cloud system resolving resolutions of 10- to 1-km globally.

Putman, William↗

Cirrus Cloud Modeling: Overview and Issues

A review of cirrus cloud modeling will be given with special attention to the role of dynamical processes in regulating cloud microphysical properties and the interactions with radiative process in determining cloud lifecycle. The talk will draw heavily on the papers by Starr and Quante, Quante and Starr and Demoz et al., as well as recent results from the GEWEX Cloud System Study (GCSS) Working Group on Cirrus Cloud Systems (WG2) Idealized Cirrus Model Comparison and Cirrus Parcel Model Comparison projects, as described in Starr et al. and Lin et al. Key issues in current cirrus cloud modeling will be described and discussed.

Starr, David OC.↗

6 CM OH absorption in megamaser galaxies

Absorption in the 2Pi sub 1/2 J = 1/2 Lambda doublet transitions of OH, 182 K above the ground state, is detected in the megamaser galaxies IC 4553 (Arp 220), MK 231, MK 273, MGC 3690, and IRAS 17208-0014. The 4660, 4751, and 4766 MHz lines have intensity ratios moderately deviating from the LTE values (1:2:1). The OH rotational temperatures appear to be close to the temperature of the dust, approx. 60 K. The common characteristics of these galaxies (absence of 6 cm inversion, the optical depths, the infrared properties, the systematic trends in the line parameters, and the rotational temperatures) all suggest that the same pump process is responsible for the 18 cm line inversion in the five megamaser sources. The inversion is probably not due to an excitation mechanism involving collisions with HI or H2. While excitation via photodissociation of H2O cannot entirely be ruled out, the most likely mechanism is considered to be to be a combination of the intense FIR field (populating higher excited OH rotational states) and the non-thermal radiation from the nuclei of the parent galaxies (affecting the excitation within the Lambda -doublets). According to an LVG model of the OH excitation of IC4553, the OH-cloud(s) have to be located close, within 200 to 300 pc, to the center of the galaxy. The excitation of the individual 18 cm lines depends critically on the effective background radiation field and hence on the galactocentric distance of the masing clump. With increasing distance first the 1720 MHz and then the 18 cm main line inversion is quenched, while 1612 MHz inversion is obtained up to approx. 600 pc. The 1612 MHz satellite line is predicted to be more intense than the 1720 MHz line. A critical test for our excitation model is to observe the 2 Pi 3/2 J = 5/2 Lambda-doublet transitions which are predicted to be detectable in absorption.

Henkel, C.↗

Comparison of PARASOL Observations with Polarized Reflectances Simulated Using Different Ice Habit Mixtures

Insufficient knowledge of the habit distribution and the degree of surface roughness of ice crystals within ice clouds is a source of uncertainty in the forward light scattering and radiative transfer simulations required in downstream applications involving these clouds. The widely used MODerate Resolution Imaging Spectroradiometer (MODIS) Collection 5 ice microphysical model assumes a mixture of various ice crystal shapes with smooth-facets except aggregates of columns for which a moderately rough condition is assumed. When compared with PARASOL (Polarization and Anisotropy of Reflectances for Atmospheric Sciences coupled with Observations from a Lidar) polarized reflection data, simulations of polarized reflectance using smooth particles show a poor fit to the measurements, whereas very rough-faceted particles provide an improved fit to the polarized reflectance. In this study a new microphysical model based on a mixture of 9 different ice crystal habits with severely roughened facets is developed. Simulated polarized reflectance using the new ice habit distribution is calculated using a vector adding-doubling radiative transfer model, and the simulations closely agree with the polarized reflectance observed by PARASOL. The new general habit mixture is also tested using a spherical albedo differences analysis, and surface roughening is found to improve the consistency of multi-angular observations. It is suggested that an ice model incorporating an ensemble of different habits with severely roughened surfaces would potentially be an adequate choice for global ice cloud retrievals.

Cole, Benjamin H.↗

Recent Advancements in the Numerical Simulation of Surface Irradiance for Solar Energy Applications

This paper briefly reviews the National Renewable Energy Laboratory's recent efforts to develop all-sky solar irradiance models for solar energy applications. The Fast All-sky Radiation Model for Solar applications (FARMS) uses the simulation of clear-sky transmittance and reflectance and a parameterization of cloud transmittance and reflectance to rapidly compute broadband irradiances on horizontal surfaces. The accuracy of FARMS is comparable to that of two-stream approximation, but it is approximately 1,000 times faster. A FARMS for Narrowband Irradiance over Tilted surfaces (FARMS-NIT) has been developed to compute spectral irradiances on photovoltaic (PV) panels in 2,002 wavelength bands. FARMS-NIT has been extended to bifacial PV panels by accounting for solar radiation reaching the backside of a PV panel.

14 SOLAR ENERGY↗

Aerosol-Ice Formation Closure Pilot Study (AEROICESTUDY) Field Campaign Report

The aerosol-ice formation closure pilot study (AEROICESTUDY) was a field campaign conducted at the U.S. Department of Energy Atmospheric Radiation Measurement (ARM) user facility at the Southern Great Plains (SGP) observatory from October 7 to 28, 2019. The purpose of this campaign was to test a field observational approach for conducting an aerosol-ice formation closure study. In other words, the goal was to predict the number of ice nucleating particles (INPs) from the measurements of physical and chemical aerosol properties and compare those to measured INP number concentrations. This project was motivated by the fact that the aerosol community has widely conducted aerosol radiative closure, aerosol-cloud condensation nuclei (CCN), and CCN-droplet closure studies to test the physical models and parameterizations that cloud-resolving and climate models rely on to perform reliable simulations of the Earth system and energy budget. However, very few closure studies related to INPs have been conducted, and to our knowledge, none using robust, size-resolved, ambient aerosol composition measurements as model inputs

AEROICESTUDY↗

Lagrangian and Eulerian Supersaturation Statistics in Turbulent Cloudy Rayleigh–Bénard Convection: Applications for LES Subgrid Modeling

Abstract Turbulent fluctuations of scalar and velocity fields are critical for cloud microphysical processes, e.g., droplet activation and size distribution evolution, and can therefore influence cloud radiative forcing and precipitation formation. Lagrangian and Eulerian water vapor, temperature, and supersaturation statistics are investigated in direct numerical simulations (DNS) of turbulent Rayleigh–Bénard convection in the Pi Convection Cloud Chamber to provide a foundation for parameterizing subgrid-scale fluctuations in atmospheric models. A subgrid model for water vapor and temperature variances and covariance and supersaturation variance is proposed, valid for both clear and cloudy conditions. Evaluation of phase change contributions through an a priori test using DNS data shows good performance of the model. Supersaturation is a nonlinear function of temperature and water vapor, and relative external fluxes of water vapor and heat (e.g., during entrainment-mixing and phase change) influence turbulent supersaturation fluctuations. Although supersaturation has autocorrelation and structure functions similar to the independent scalars (temperature and water vapor), the autocorrelation time scale of supersaturation differs. Relative scalar fluxes in DNS without cloud make supersaturation PDFs less skewed than the adiabatic case, where they are highly negatively skewed. However, droplet condensation changes the PDF shape response: it becomes positively skewed for the adiabatic case and negatively skewed when the sidewall relative fluxes are large. Condensation also increases correlations between water vapor and temperature in the presence of relative scalar fluxes but decreases correlations for the adiabatic case. These changes in correlation suppress supersaturation variability for the nonadiabatic cases and increase it for the adiabatic case. Implications of this work for subgrid microphysics modeling using a Lagrangian stochastic scheme are also discussed.

54 ENVIRONMENTAL SCIENCES↗

Satellite-Surface Perspectives of Air Quality and Aerosol-Cloud Effects on the Environment: An Overview of 7-SEAS BASELInE

The objectives of 7-SEASBASELInE (Seven SouthEast Asian Studies Biomass-burning Aerosols and Stratocumulus Environment: Lifecycles and Interactions Experiment) campaigns in spring 2013-2015 were to synergize measurements from uniquely distributed ground-based networks (e.g., AERONET (AErosol RObotic NETwork)), MPLNET ( NASA Micro-Pulse Lidar Network)) and sophisticated platforms (e.g.,SMARTLabs (Surface-based Mobile Atmospheric Research and Testbed Laboratories), regional contributing instruments), along with satellite observations retrievals and regional atmospheric transport chemical models to establish a critically needed database, and to advance our understanding of biomass-burning aerosols and trace gases in Southeast Asia (SEA). We present a satellite-surface perspective of 7-SEASBASELInE and highlight scientific findings concerning: (1) regional meteorology of moisture fields conducive to the production and maintenance of low-level stratiform clouds over land; (2) atmospheric composition in a biomass-burning environment, particularly tracers-markers to serve as important indicators for assessing the state and evolution of atmospheric constituents; (3) applications of remote sensing to air quality and impact on radiative energetics, examining the effect of diurnal variability of boundary-layer height on aerosol loading; (4) aerosol hygroscopicity and ground-based cloud radar measurements in aerosol-cloud processes by advanced cloud ensemble models; and (5) implications of air quality, in terms of toxicity of nanoparticles and trace gases, to human health. This volume is the third 7-SEAS special issue (after Atmospheric Research, vol. 122, 2013; and Atmospheric Environment, vol. 78, 2013) and includes 27 papers published, with emphasis on air quality and aerosol-cloud effects on the environment. BASELInE observations of stratiform clouds over SEA are unique, such clouds are embedded in a heavy aerosol-laden environment and feature characteristically greater stability over land than over ocean, with minimal radar surface clutter at a high vertical spatial resolution. To facilitate an improved understanding of regional aerosol-cloud effects, we envision that future BASELInE-like measurement modeling needs fall into two categories: (1) efficient yet critical in-situ profiling of the boundary layer for validating remote-sensing retrievals and for initializing regional transport chemical and cloud ensemble models; and (2) fully utilizing the high observing frequencies of geostationary satellites for resolving the diurnal cycle of the boundary layerheight as it affects the loading of biomass-burning aerosols, air quality and radiative energetics.

AERONET↗

The potential role of organics in new particle formation and initial growth in the remote tropical upper troposphere

Abstract. Global observations and model studies indicate that new particle formation (NPF) in the upper troposphere (UT) and subsequent particles supply 40 %–60 % of cloud condensation nuclei (CCN) in the lower troposphere, thus affecting the Earth's radiative budget. There are several plausible nucleation mechanisms and precursor species in this atmospheric region, which, in the absence of observational constraints, lead to uncertainties in modeled aerosols. In particular, the type of nucleation mechanism and concentrations of nucleation precursors, in part, determine the spatial distribution of new particles and resulting spatial distribution of CCN from this source. Although substantial advances in understanding NPF have been made in recent years, NPF processes in the UT in pristine marine regions are still poorly understood and are inadequately represented in global models. Here, we evaluate commonly used and state-of-the-art NPF schemes in a Lagrangian box model to assess which schemes and precursor concentrations best reproduce detailed in situ observations. Using measurements of aerosol size distributions (0.003 < Dp < 4.8 µm) in the remote marine troposphere between ∼0.18 and 13 km altitude obtained during the NASA Atmospheric Tomography (ATom) mission, we show that high concentrations of newly formed particles in the tropical UT over both the Atlantic and Pacific oceans are associated with outflow regions of deep convective clouds. We focus analysis on observations over the remote Pacific Ocean, which is a region less perturbed by continental emissions than the Atlantic. Comparing aerosol size distribution measurements over the remote Pacific with box model simulations for 32 cases shows that none of the NPF schemes most commonly used in global models, including binary nucleation of sulfuric acid and water (neutral and ion-assisted) and ternary involving sulfuric acid, water, and ammonia, are consistent with observations, regardless of precursor concentrations. Through sensitivity studies, we find that the nucleation scheme among those tested that is able to explain most consistently (21 of 32 cases) the observed size distributions is that of Riccobono et al. (2014), which involves both organic species and sulfuric acid. The method of Dunne et al. (2016), involving charged sulfuric acid–water–ammonia nucleation, when coupled with organic growth of the nucleated particles, was most consistent with the observations for 5 of 32 cases. Similarly, the neutral sulfuric acid–water–ammonia method of Napari (2002), when scaled with a tuning factor and with organic growth added, was most consistent for 6 of 32 cases. We find that to best reproduce both nucleation and growth rates, the mixing ratios of gas-phase organic precursors generally need to be at least twice that of SO2, a proxy for dimethyl sulfide (DMS). Unfortunately, we have no information on the nature of oxidized organic species that participated in NPF in this region. Global models rarely include organic-driven nucleation and growth pathways in UT conditions where globally significant NPF takes place, which may result in poor estimates of NPF and CCN abundance and contribute to uncertainties in aerosol–cloud–radiation effects. Furthermore, our results indicate that the organic aerosol precursor vapors may be important in the tropical UT above marine regions, a finding that should guide future observational efforts.

54 ENVIRONMENTAL SCIENCES↗

ARM West Antarctic Radiation Experiment (AWARE) Field Campaign Report

The U.S. Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) West Antarctic Radiation Experiment (AWARE) is the most technologically advanced atmospheric and climate science campaign yet fielded in Antarctica. AWARE was motivated be recent concern about the impact of cryospheric mass loss on global sea level rise. Specifically, the West Antarctic Ice Sheet (WAIS) is now the second largest contributor to rising sea level, after the Greenland Ice Sheet. As steadily warming ocean water erodes the grounding lines of WAIS components where they meet the Amundsen and Bellingshausen Seas, the retreating grounding lines moving inland and downslope on the underlying terrain imply mechanical instability of the entire WAIS. There is evidence that this point of instability may have already been reached, perhaps signifying more rapid loss of WAIS ice mass. At the same time, the mechanical support provided by adjacent ice shelves, and also the fundamental stability of exposed ice cliffs at the ice sheet grounding lines, will be adversely impacted by a warming atmosphere that causes more frequent episodes of surface melting. The surface meltwater damages the ice shelves and ice cliffs through hydrofracturing. With the increasing concern regarding these rapid cryospheric changes, AWARE was motivated by the need to (a) diagnose the surface energy balance in West Antarctica as related to both summer season climatology and potential surface melting, and (b) improve global climate model (GCM) performance over Antarctica, such that future cryospheric projections can be more reliable.

aerosol observing system↗

C II 158 micron and O I 63 micron observations of NGC 7023 - A model for its photodissociation region

Emission in the far IR fine-structure lines of O I (63 microns) and C II (158 microns) from the bright optical reflection nebula NGC 7023 has been observed. It is suggested that this emission arises in a warm, atomic photodissociation region produced by the interaction of the UV radiation of the illuminating star with a molecular cloud. The density and temperature in the photodissociation region is estimated and a model for the region is constructed.

Chokshi, A.↗

Sensitivity of aerosol optical properties to the aerosol size distribution over central Europe and the Mediterranean Basin using the WRF-Chem v.3.9.1.1 coupled model

The size distribution of atmospheric aerosols plays a key role for understanding and quantifying the uncertainties related to aerosol–radiation and aerosol–cloud interactions. These interactions ultimately depend on the size distribution through optical properties (such as aerosol optical depth, AOD) or cloud microphysical properties. Hence, the main objective of this contribution is to disentangle the impact of the representation of aerosol size distribution on aerosol optical properties over central Europe, particularly over the Mediterranean Basin, during a summertime aerosol episode. To fulfill this objective, a sensitivity test has been conducted using the coupled chemistry–meteorology model WRF-Chem (Weather Research Forecast model coupled with Chemistry). The test modified the parameters defining a lognormal size distribution (geometric diameter and standard deviation) by 10 %, 20 %, and 50 %. Results reveal that the reduction in the standard deviation of the accumulation mode leads to the largest impacts on AOD due to a transfer of particles from the accumulation mode to the coarse mode. A reduction in the geometric diameter of the accumulation mode also has an influence on AOD representation since particles in this mode are assumed to be smaller. In addition, an increase in the geometric diameter of the coarse mode produces a redistribution through the total size distribution by relocating particles from the finer modes to the coarse.

54 ENVIRONMENTAL SCIENCES↗

Effect of Thin Cirrus Clouds on Dust Optical Depth Retrievals From MODIS Observations

The effect of thin cirrus clouds in retrieving the dust optical depth from MODIS observations is investigated by using a simplified aerosol retrieval algorithm based on the principles of the Deep Blue aerosol property retrieval method. Specifically, the errors of the retrieved dust optical depth due to thin cirrus contamination are quantified through the comparison of two retrievals by assuming dust-only atmospheres and the counterparts with overlapping mineral dust and thin cirrus clouds. To account for the effect of the polarization state of radiation field on radiance simulation, a vector radiative transfer model is used to generate the lookup tables. In the forward radiative transfer simulations involved in generating the lookup tables, the Rayleigh scattering by atmospheric gaseous molecules and the reflection of the surface assumed to be Lambertian are fully taken into account. Additionally, the spheroid model is utilized to account for the nonsphericity of dust particles In computing their optical properties. For simplicity, the single-scattering albedo, scattering phase matrix, and optical depth are specified a priori for thin cirrus clouds assumed to consist of droxtal ice crystals. The present results indicate that the errors in the retrieved dust optical depths due to the contamination of thin cirrus clouds depend on the scattering angle, underlying surface reflectance, and dust optical depth. Under heavy dusty conditions, the absolute errors are comparable to the predescribed optical depths of thin cirrus clouds.

Feng, Qian↗

Overview and Statistical Analysis of Boundary Layer Clouds and Precipitation Over the Western North Atlantic Ocean

Due to their fast evolution and large natural variability in macro- and microphysical properties, the accurate representation of boundary layer clouds in current climate models remains a challenge. One of the regions with large intermodel spread in the Coupled Model Intercomparison Project Phase 6 ensemble is the western North Atlantic Ocean. Here, statistically representative in situ measurements can help to develop and constrain the parameterization of clouds in global models. To this end, we performed comprehensive measurements of boundary layer clouds, aerosol, trace gases, and radiation in the western North Atlantic Ocean during the NASA Aerosol Cloud meTeorology Interactions oVer the western ATlantic Experiment (ACTIVATE) mission. In total, 174 research flights with 574 flight hours for cloud and precipitation measurements were performed with the HU-25 Falcon during three winter (February–March 2020, January–April 2021, and November 2021–March 2022) and three summer seasons (August–September 2020, May–June 2021, and May–June 2022). Here we present a statistical evaluation of 16 140 individual cloud events probed by the fast cloud droplet probe and the two-dimensional stereo cloud probe during 155 research flights in a representative and repetitive flight strategy allowing for robust statistical data analyses. We show that the vertical profiles of distributions of the liquid water content and the cloud droplet effective diameter (ED) increase with altitude in the marine boundary layer. Due to higher updraft speeds, higher cloud droplet number concentrations (N liquid ) were measured in winter compared to summer despite lower cloud condensation nucleus abundance. Flight cloud cover derived from statistical analysis of in situ data is reduced in summer and shows large variability. This seasonal contrast in cloud coverage is consistent with a dominance of a synoptic pattern in winter that favors conditions for the formation of stratiform clouds at the western edge of cyclones (post-cyclonic). In contrast, a dominant summer anticyclone is concomitant with the occurrence of shallow cumulus clouds and lower cloud coverage. The evaluation of boundary layer clouds and precipitation in the N liquid ED phase space sheds light on liquid, mixed-phase, and ice cloud properties and helps to categorize the cloud data. Ice and liquid precipitation, often masked in cloud statistics by a high abundance of liquid clouds, is often observed throughout the cloud. The ACTIVATE in situ cloud measurements provide a wealth of cloud information useful for assessing airborne and satellite remote-sensing products, for global climate and weather model evaluations, and for dedicated process studies that address precipitation and aerosol–cloud interactions.

Aerosol↗

Using Neural Networks to Improve the Performance of Radiative Transfer Modeling Used for Geometry Dependent Surface Lambertian-Equivalent Reflectivity Calculations

Surface Lambertian-equivalent reflectivity (LER) is important for trace gas retrievals in the direct calculation of cloud fractions and indirect calculation of the air mass factor. Current trace gas retrievals use climatological surface LER's. Surface properties that impact the bidirectional reflectance distribution function (BRDF) as well as varying satellite viewing geometry can be important for retrieval of trace gases. Geometry Dependent LER (GLER) captures these effects with its calculation of sun normalized radiances (I/F) and can be used in current LER algorithms (Vasilkov et al. 2016). Pixel by pixel radiative transfer calculations are computationally expensive for large datasets. Modern satellite missions such as the Tropospheric Monitoring Instrument (TROPOMI) produce very large datasets as they take measurements at much higher spatial and spectral resolutions. Look up table (LUT) interpolation improves the speed of radiative transfer calculations but complexity increases for non-linear functions. Neural networks perform fast calculations and can accurately predict both non-linear and linear functions with little effort.

Geometry Dependent LER (GLER) capture↗