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At least 91 records · Page 5

A Coupled GCM-Cloud Resolving Modeling System to Study Precipitation Processes

Recent GEWEX Cloud System Study (GCSS) model comparison projects have indicated that cloud resolving models (CRMs) agree with observations better than traditional single column models in simulating various types of clouds and cloud systems from different geographic locations. Current and future NASA satellite programs can provide cloud, precipitation, aerosol and other data at very fine spatial and temporal scales. It requires a coupled global circulation model (GCM) and cloud-scale model (termed a super-parameterization or multi-scale modeling framework, MMF) to use these satellite data to improve the understanding of the physical processes that are responsible for the variation in global and regional climate and hydrological systems. The use of a GCM will enable global coverage and the use of a CRM will allow for better and more sophisticated physical parameterization. NASA Satellite and field campaign cloud related data sets can provide initial conditions as well as validation for both the MMF and CRMs. Also we have implemented a Land Information System (LIS that includes the CLM and NOAH land surface models into the MMF. The Goddard MMF is based on the 2D Goddard Cumulus Ensemble (GCE) model and the Goddard finite volume general circulation model (fvGCM) This modeling system has been applied and tested its performance for two different climate scenarios, El Nino (1998) and La Nina (1999). The coupled new modeling system produced more realistic propagation and intensity of tropical rainfall systems and intraseasonal oscillations, and diurnal variation of precipitation that are very difficult to forecast using even the state-of-the-art GCMs. In this talk I will present: (1) a brief review on GCE model and its applications on precipitation processes (both Microphysical and land processes) and (2) The Goddard MMF and the Major difference between two existing MMFs (CSU MMF and Goddard MMF) and preliminary results (the comparison with traditional GCMs).

Tao, Wei-Kuo↗

A Coupled GCM-Cloud Resolving Modeling System, and a Regional Scale Model to Study Precipitation Processes

Recent GEWEX Cloud System Study (GCSS) model comparison projects have indicated that cloud-resolving models (CRMs) agree with observations better than traditional single-column models in simulating various types of clouds and cloud systems from different geographic locations. Current and future NASA satellite programs can provide cloud, precipitation, aerosol and other data at very fine spatial and temporal scales. It requires a coupled global circulation model (GCM) and cloud-scale model (termed a superparameterization or multi-scale modeling framework, MMF) to use these satellite data to improve the understanding of the physical processes that are responsible for the variation in global and regional climate and hydrological systems. The use of a GCM will enable global coverage, and the use of a CRM will allow for better and more sophisticated physical parameterization. NASA satellite and field campaign cloud related datasets can provide initial conditions as well as validation for both the MMF and CRMs. The Goddard MMF is based on the 2D Goddard Cumulus Ensemble (GCE) model and the Goddard finite volume general circulation model (fvGCM), and it has started production runs with two years results (1998 and 1999). Also, at Goddard, we have implemented several Goddard microphysical schemes (2ICE, several 31CE), Goddard radiation (including explicitly calculated cloud optical properties), and Goddard Land Information (LIS, that includes the CLM and NOAH land surface models) into a next generatio11 regional scale model, WRF. In this talk, I will present: (1) A brief review on GCE model and its applications on precipitation processes (microphysical and land processes), (2) The Goddard MMF and the major difference between two existing MMFs (CSU MMF and Goddard MMF), and preliminary results (the comparison with traditional GCMs), and (3) A discussion on the Goddard WRF version (its developments and applications).

Tao, Wei-Kuo↗

A Coupled GCM-Cloud Resolving Modeling System, and A Regional Scale Model to Study Precipitation Processes

Recent GEWEX Cloud System Study (GCSS) model comparison projects have indicated that cloud-resolving models (CRMs) agree with observations better than traditional single-column models in simulating various types of clouds and cloud systems from different geographic locations. Current and future NASA satellite programs can provide cloud, precipitation, aerosol and other data at very fine spatial and temporal scales. It requires a coupled global circulation model (GCM) and cloud-scale model (termed a super-parameterization or multi-scale modeling framework, MMF) to use these satellite data to improve the understanding of the physical processes that are responsible for the variation in global and regional climate and hydrological systems. The use of a GCM will enable global coverage, and the use of a CRM will allow for better and more sophisticated physical parameterization. NASA satellite and field campaign cloud related datasets can provide initial conditions as well as validation for both the MMF and CRMs. The Goddard MMF is based on the 2D Goddard Cumulus Ensemble (GCE) model and the Goddard finite volume general circulation model (fvGCM), and it has started production runs with two years results (1 998 and 1999).

Tao, Wei-Kuo↗

Longwave Band-by-band Cloud Radiative Effect and its Application in GCM Evaluation

The cloud radiative effect (CRE) of each longwave (LW) absorption band of a GCM fs radiation code is uniquely valuable for GCM evaluation because (1) comparing band-by-band CRE avoids the compensating biases in the broadband CRE comparison and (2) the fractional contribution of each band to the LW broadband CRE (f(sub CRE)) is sensitive to cloud top height but largely insensitive to cloud fraction, presenting thus a diagnostic metric to separate the two macroscopic properties of clouds. Recent studies led by the first author have established methods to derive such band ]by ]band quantities from collocated AIRS and CERES observations. We present here a study that compares the observed band-by-band CRE over the tropical oceans with those simulated by three different atmospheric GCMs (GFDL AM2, NASA GEOS-5, and CCCma CanAM4) forced by observed SST. The models agree with observation on the annual ]mean LW broadband CRE over the tropical oceans within +/-1W/sq m. However, the differences among these three GCMs in some bands can be as large as or even larger than +/-1W/sq m. Observed seasonal cycles of f(sub CRE) in major bands are shown to be consistent with the seasonal cycle of cloud top pressure for both the amplitude and the phase. However, while the three simulated seasonal cycles of f(sub CRE) agree with observations on the phase, the amplitudes are underestimated. Simulated interannual anomalies from GFDL AM2 and CCCma CanAM4 are in phase with observed anomalies. The spatial distribution of f(sub CRE) highlights the discrepancies between models and observation over the low-cloud regions and the compensating biases from different bands.

Huang, Xianglei↗

The MJO Transition from Shallow to Deep Convection in CloudSat/CALIPSO Data and GISS GCM Simulations

The relationship between convective penetration depth and tropospheric humidity is central to recent theories of the Madden-Julian oscillation (MJO). It has been suggested that general circulation models (GCMs) poorly simulate the MJO because they fail to gradually moisten the troposphere by shallow convection and simulate a slow transition to deep convection. CloudSat and Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) data are analyzed to document the variability of convection depth and its relation to water vapor during the MJO transition from shallow to deep convection and to constrain GCM cumulus parameterizations. Composites of cloud occurrence for 10MJO events show the following anticipatedMJO cloud structure: shallow and congestus clouds in advance of the peak, deep clouds near the peak, and upper-level anvils after the peak. Cirrus clouds are also frequent in advance of the peak. The Advanced Microwave Scanning Radiometer for EarthObserving System (EOS) (AMSR-E) columnwater vapor (CWV) increases by;5 mmduring the shallow- deep transition phase, consistent with the idea of moisture preconditioning. Echo-top height of clouds rooted in the boundary layer increases sharply with CWV, with large variability in depth when CWV is between;46 and 68 mm. International Satellite Cloud Climatology Project cloud classifications reproduce these climatological relationships but correctly identify congestus-dominated scenes only about half the time. A version of the Goddard Institute for Space Studies Model E2 (GISS-E2) GCM with strengthened entrainment and rain evaporation that produces MJO-like variability also reproduces the shallow-deep convection transition, including the large variability of cloud-top height at intermediate CWV values. The variability is due to small grid-scale relative humidity and lapse rate anomalies for similar values of CWV. 1.

DelGenio, Anthony G.↗

A Two-Habit Ice Cloud Optical Property Parameterization for GCM Application

We present a novel ice cloud optical property parameterization based on a two-habit ice cloud model that has been proved to be optimal for remote sensing applications. The two-habit ice model is developed with state-of-the-art numerical methods for light scattering property calculations involving individual columns and column aggregates with the habit fractions constrained by in-situ measurements from various field campaigns. Band-averaged bulk ice cloud optical properties including the single-scattering albedo, the mass extinction/absorption coefficients, and the asymmetry factor are parameterized as functions of the effective particle diameter for the spectral bands involved in the broadband radiative transfer models. Compared with other parameterization schemes, the two-habit scheme generally has lower asymmetry factor values (around 0.75 at the visible wavelengths). The two-habit parameterization scheme was widely tested with the broadband radiative transfer models (i.e. Rapid Radiative Transfer Model, GCM version) and global circulation models (GCMs, i.e. Community Atmosphere Model, version 5). Global ice cloud radiative effects at the top of the atmosphere are also analyzed from the GCM simulation using the two-habit parameterization scheme in comparison with CERES satellite observations.

Yi, Bingqi↗

(GO)2-SIM: a GCM-Oriented Ground-Observation Forward-Simulator Framework for Objective Evaluation of Cloud and Precipitation Phase

General circulation model (GCM) evaluation using ground-based observations is complicated by inconsistencies in hydrometeor and phase definitions. Here we describe (GO)2-SIM, a forward simulator designed for objective hydrometeor-phase evaluation, and assess its performance over the North Slope of Alaska using a 1-year GCM simulation. For uncertainty assessment, 18 empirical relationships are used to convert model grid-average hydrometeor (liquid and ice, cloud, and precipitation) water contents to zenith polarimetric micropulse lidar and Ka-band Doppler radar measurements, producing an ensemble of 576 forward-simulation realizations. Sensor limitations are represented in forward space to objectively remove from consideration model grid cells with undetectable hydrometeor mixing ratios, some of which may correspond to numerical noise.Phase classification in forward space is complicated by the inability of sensors to measure ice and liquid signals distinctly. However, signatures exist in lidar–radar space such that thresholds on observables can be objectively estimated and related to hydrometeor phase. The proposed phase-classification technique leads to misclassification in fewer than 8% of hydrometeor-containing grid cells. Such misclassifications arise because, while the radar is capable of detecting mixed-phase conditions, it can mistake water- for ice-dominated layers. However, applying the same classification algorithm to forward-simulated and observed fields should generate hydrometeor-phase statistics with similar uncertainty. Alternatively, choosing to disregard how sensors define hydrometeor phase leads to frequency of occurrence discrepancies of up to 40%. So, while hydrometeor-phase maps determined in forward space are very different from model "reality" they capture the information sensors can provide and thereby enable objective model evaluation.

Lamer, K.↗

P43K-3884 Characterizing Martian Crater Circulations with the NASA Ames Mars GCM

Observations made in Gale Crater by instruments on the MSL Curiosity Rover show that the diurnal amplitude of the surface pressure is increased and the depth of the Convective Boundary Layer (CBL) is decreased relative to other lander locations on flatter regions of Mars (Haberle et al., 2014; Moores et al., 2015). Mesoscale modeling studies of Gale Crater suggest that crater circulations produce these effects. Tyler & Barnes (2013) show that local upslope/downslope flows along the crater rim and Mt. Sharp amplify the diurnal pressure cycle. These same flows are thought to be at least partly responsible for the suppression of the CBL because upward air flow at the rim and in the center (due to Mt. Sharp) forces subsidence over the lowest regions of the crater during the day. Regional flows, largely due to the location of Gale near the dichotomy boundary, may also play a role in shaping the circulation internal to the crater. Whether the behavior of the CBL and the amplified diurnal pressure cycle are phenomena observed in craters morphologically different from Gale (i.e. bowl-shaped, irregular, degraded) is not yet understood. We will explore these questions by characterizing the behavior of these processes as they are shaped by the morphology of craters greater than 100 km in diameter. We use the NASA Ames Mars Global Circulation Model (GCM) that now utilizes the NOAA/GFDL cubed-sphere finite-volume dynamical core to examine ~100 craters of varying size and shape from a database of known Martian craters (Robbins & Hynek, 2014). Run at 7.5 km resolution, the GCM is capable of resolving surface winds, temperature, and pressure inside craters of this size allowing for the analysis of dozens of craters simulated at various seasons and within the context of synoptic and global-scale phenomena.

Batterson, Courtney MaryLou↗

Generating a 4D Global CH(4) Product by Assimilating TROPOMI column CH(4) in NASA’s GEOS GCM

Examination of temporal and spatial CH4 variability is crucial for better understanding the human and natural processes driving climate change and ultimately designing mitigation strategies. Here we present an analysis framework that uses NASA’s GEOS General Circulation Model (GCM) to construct a high-resolution, time varying picture of atmospheric CH4 consistent with measurements from a variety of platforms, both in situ and remotely sensed. The resulting time varying atmospheric CH4 product can (i) support interpretation of high-resolution point source detection approaches, (ii) provide reanalysis fields for CH4 and other greenhouse gases, and (iii) supply boundary conditions for regional models. Our approach starts with a set of CH4 emissions from various inventories that have been adjusted to match the global annual growth rate over recent decades. These emissions are transported by the GEOS GCM, which in turn is constrained by meteorology from NASA’s Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2) product. The simulated atmospheric field is compared with CH4 measurements, such as those from the TROPOspheric Monitoring Instrument (TROPOMI), and adjustments calculated following a Bayesian protocol. The accuracy of the resultant optimal atmospheric CH4 field can be demonstrated by its improved agreement (compared to a direct simulation of the CH4 inventories) with a host of independent CH4 measurements, such as those from the Total Carbon Column Observation Network (TCCON) and in situ observations from surface and airborne platforms.

Nikolay V. Balashov↗

Investigating the Causes and Impacts of Convective Aggregation in a High Resolution Atmospheric GCM

Abstract A ∼50 km resolution atmospheric general circulation model (GCM) is used to investigate the impact of radiative interactions on spatial organization of convection, the model's mean state, and extreme precipitation events in the presence of realistic boundary conditions. Mechanism‐denial experiments are performed in which synoptic‐scale feedbacks between radiation and dynamics are suppressed by overwriting the model‐generated atmospheric radiative cooling rates with its monthly varying climatological values. When synoptic‐scale radiative interactions are disabled, the annual mean circulation and precipitation remain almost unchanged, however tropical convection becomes less aggregated, with an increase in cloud fraction and relative humidity in the free troposphere but a decrease in both variables in the boundary layer. Changes in cloud fraction and relative humidity in the boundary layer exhibit more sensitivity to the presence of radiative interactions than variations in the degree of aggregation. The less aggregated state is associated with a decrease in the frequency of extreme precipitation events, coincident with a decrease in the dynamical contribution to the magnitude of extreme precipitation. At regional scales, the spatial contrast in radiative cooling between dry and moist regions diminishes when radiative interactions are suppressed, reducing the upgradient transport of energy, degree of aggregation, and frequency of extreme precipitation events. However, the mean width of the tropical rain belt remains almost unaffected when radiative interactions are disabled. These results offer insights into how radiation‐circulation coupling affects the spatial organization of convection, distributions of clouds and humidity, and weather extremes.

54 ENVIRONMENTAL SCIENCES↗

Evolving CO 2 rather than SST leads to a factor of ten decrease in GCM convergence time

The high computational cost of Global Climate Models (GCMs) is a problem that limits their use in many areas. Recently an inverse climate modeling (InvCM) method, which fixes the global mean sea surface temperature (SST) and evolves the CO 2 mixing ratio to equilibrate climate, has been implemented in a cloud resolving model. In this paper, we apply InvCM to ExoCAM GCM aquaplanet simulations, allowing the SST pattern to evolve while maintaining a fixed global-mean SST. We find that InvCM produces the same climate as normal slab-ocean simulations but converges an order of magnitude faster. We then use InvCM to calculate the equilibrium CO 2 for SSTs ranging from 290 K to 340 K at 1 K intervals and reproduce the large increase in climate sensitivity at an SST of about 315 K at much higher temperature resolution. The speedup provided by InvCM could be used to equilibrate GCMs at higher spatial resolution or to perform broader parameter space exploration in order to gain new insight into the climate system. Additionally, InvCM could be used to find unstable and hidden climate states, and to find climate states close to bifurcations such as the runaway greenhouse transition.

54 ENVIRONMENTAL SCIENCES↗

A Decadal Hybrid GCM Simulation Using Deep‐Learning‐Based Cloud and Convection Parameterization Generalized to a Warm Climate

A critical challenge for machine‐learning (ML) parameterization in global climate models (GCMs) is to achieve stable, accurate simulations under climates not seen during training. Previous studies have demonstrated promising offline performance and year‐long online stability in aquaplanet simulations but have encountered difficulties in real geography and under climate warming. Here we report that a GCM with real geography configuration using neural‐network‐based cloud and convection parameterization, trained exclusively with present‐day climate data, successfully performs a stable, decade‐long simulation of a warm climate with +4 K sea surface temperature (SST). The neural network (NN) is based on Han et al. (2023, https://doi.org/10.1029/2022ms003508 ) with additional inputs. The simulation captures the global precipitation distribution, surface temperatures, vertical atmospheric structures, and extreme precipitation very well, closely matching simulations from both the superparameterized CAM (SPCAM) and the conventional CAM5 in the warm climate without accuracy degradation compared to those in the baseline climate. Moreover, it produces a climate response to +4 K SST in atmospheric thermodynamic states and circulations similar to those from SPCAM and CAM5. Prognostic ablation tests on NN input variables show that the NN without convective memory as input suffers from numerical instability, and the NN without considering radiative variables and land fraction as input, or with reduced training samples produce less accurate results. To our knowledge, this is the first time an ML parameterization successfully achieves online extrapolation to a warm climate without using additional warm‐climate data for training. It demonstrates the potential of ML‐driven parameterizations for credible long‐term climate projections.

Atmosphere model↗

Improving GCM Representation of Convective Cloud Microphysics by Using ARM Raman Lidar and Cloud Radar Observations

The overall objective of this Department of Energy (DOE) Atmospheric System Research (ASR) funded project is to improve the representation of convective cloud microphysics in global climate models (GCMs) and check it by comparing the model simulations with observations. We have derived the cloud ice water content by synthesizing ARM Raman lidar (RL) and cloud radar observations at the Atmospheric Radiation Measurement (ARM) sites. Noting that the simulated anvil clouds in terms of their macro- and micro-physical properties are sensitive to the parameterization of convective microphysical processes, observed ice water content in anvil clouds provides a useful constraint on these parameterizations. We have improved the convective microphysics parameterization scheme by (1) considering sedimentation for cloud ice crystals that do not fall in the original scheme, (2) applying a new terminal velocity parameterization that depends on the environmental conditions for convective snow, (3) adding a new hydrometeor category, “rimed ice,” to the original four-class (cloud liquid, cloud ice, rain, and snow) scheme, and (4) allowing convective clouds to detrain snow particles into stratiform clouds. We have examined the impact of improved convective cloud microphysics parameterization on the simulated global climate from GCM simulations.

54 ENVIRONMENTAL SCIENCES↗

Improving GCM Predictability of Mixed-Phase Clouds and Aerosol Interactions at High Latitudes with ARM Observations

The goal of this project is to improve the predictability of mixed-phase clouds and aerosol interactions in the Community Atmosphere Model version 6 (CAM6) through comparison with the ARM observations. There are three main objectives of the proposed study: (1) Improve the representation of ice microphysical processes in mixed-phase clouds; (2) Test the performance of ice microphysics in CESM-CAM6 with the ARM observations in northern and southern high latitudes; and (3) Examine mixed-phase cloud microphysics-aerosol-turbulence-radiation interactions in CESM-CAM6. In this project, we have (1) Improved the representation of ice microphysical processes in mixed-phase clouds in CESM-CAM6 by implementing the marine organic aerosol (MOA) and treating the ice nucleating particles (INPs) from MOA and its impacts on mixed-phase clouds. We made a first attempt to represent different secondary ice production (SIP) mechanisms in a GCM (CESM2-CAM6). We found that misrepresentation of these ice formation processes in global climate models (GCMs) leads to too weak negative cloud feedback over the Southern Ocean (SO) and too high climate sensitivity in the models. In addition to ice formation processes, we improved the treatment of ice depositional growth through the Wegener–Bergeron–Findeisen (WBF) process by considering the subgrid heterogeneous distributions between liquid droplets and ice crystals in mixed-phase clouds; (2) Tested the performance of our improved representations of ice microphysics with the ARM observations at high latitudes.

54 ENVIRONMENTAL SCIENCES↗

GCAM v4.3 SSP-RCP-GCM Output Products

Supplemental dataset to: Graham N.T., M.I. Hejazi, M. Chen, E. Davies, J.A. Edmonds, S.H. Kim, and S. Turner, et al. 2020. "Humans drive future water scarcity changes across all Shared Socioeconomic Pathways." Environmental Research Letters 15, no. 1:Article No. 014007. PNNL-SA-151297. doi:10.1088/1748-9326/ab639b This analysis makes deterministic classifications of how, when water resources are limited and constrained, the human and climate systems interact. The relative effects of both systems on water scarcity are quantified at global and basin scales across 15 global futures that include five different socioeconomic conditions (the Shared Socioeconomic Pathways, SSPs) and four different climatic conditions (the Representative Concentration Pathways, RCPs). These 15 scenarios are used to first analyze a 'Human Alone' component by isolating the human impact on future scarcity. This is accomplished by holding all climate variables to their 2005 levels while altering socioeconomic growth and technological change. General circulation model (GCM) derived climate impacts for five models are applied to establish 75 'Human and Climate' scenarios which allows for the quantification of climate impacts. Climatic impacts to water supply, agricultural productivity and change, hydropower availability, and building energy demands are applied from 5 different bias-corrected GCMs to make a suite of 75 climate runs. By subtracting the human derived impacts from the 'Human Alone' scenarios, from the 'Human and Climate' scenarios the climate impact is isolated. First, the drivers of future water scarcity are evaluated by isolating the impacts that both humans and climate have while accounting for feedbacks between humans, energy, and land. Secondly, the simultaneous impacts that human and climate systems have on water scarcity are analyzed by determining whether each system is increasing or decreasing scarcity in all global water basins. Below we describe the GCAM model, the scenario components, climate derived impacts, and the calculations of scarcity changes and attribution. This study uses the global change assessment model (GCAM), with inclusions of water constraints to both renewable and nonrenewable sources of water, to investigate the relative contributions of climate and human systems on water scarcity regionally and globally under a wide range of scenarios. GCAM links socioeconomics, the energy system, land-use change, climate, and the water sector. GCAM is a market-equilibrium model that allows for prices to be adjusted within each time step to ensure that the supply and demand of goods and services remains equilibrated at each time step allowing for simultaneous market clearing across sectors. This study accounts for a limited supply of water by employing cost resource curves across all 235 basins that follow a logit formulation to determine the share of each water source (renewable surface water, nonrenewable groundwater, and desalinated water) needed to meet the water demands within all basins. As depletion of various water sources increases the extraction price increases, which leads to compounding price increases on the goods and services that require higher-priced water sources.

99 GENERAL AND MISCELLANEOUS↗

A GCM simulation of the earth-atmosphere radiation balance for winter and summer

The radiation balance of the earth-atmosphere system simulated by using the general circulation model (GCM) of the Laboratory for Atmospheric Sciences (GLAS) is examined in regards to its graphical distribution, zonally-averaged distribution, and global mean. Most of the main features of the radiation balance at the top of the atmosphere are reasonably simulated, with some differences in the detailed structure of the patterns and intensities for both summer and winter in comparison with values as derived from Nimbus and NOAA (National Oceanic and Atmospheric Administration) satellite observations. Both the capability and defects of the model are discussed.

Wu, M. L. C.↗

Ocean fluxes simulated by the GLAS GCM

A two year run with the GLAS climate model with prescribed but seasonally varying boundary conditions provided mean monthly fluxes of sensible heat, latent heat, and radiative energy. These fluxes were analyzed to examine the energy exchange processes between the atmosphere and the ice-free ocean. A mean annual plot of monthly zonal fuxes of sensible heat, latent heat, and net radiation was produced. From these, northward transport of heat flux that would follow if the GCM simulated fluxes were consistent with oceanic circulation were produced. These results are compared with observations.

Sud, Y. C.↗

A new parameterization of 15 micron radiative transfer for a GCM

In order to make the Wu-Kaplan longwave radiative transfer parameterization (Krishnamurthy, 1982) presently used in the 9 layer GLAS GCM more suitable for use at higher horizontal and vertical resolutions, the fixed CO2 transmittance tables and climatological O3 transmittances are replaced with appropriate models. Results of off line tests of simple models of CO2 transmittance as a function of atmospheric temperature profile and surface pressure, based on the technique used by Susskind et al. (1983) in the GLAS physical retrieval scheme are given. The models are evaluated in terms of tansmittance error, flux divergence error, and equilibrium temperature error. The transmittances of CO2 averaged over each of the spectral bands 500-660 cm-1 and 660-800 cm-1 are modeled, following Susskind et al., 1983, as products of effective layer transmittances.

Wobus, R. L.↗