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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Improving Predictability of Mixed-Phase Clouds and Aerosol Interactions in the Community Earth System Model (CESM) with ARM Measurements

The objective of this project is to improve the simulation and predictability of mixed-phase clouds and aerosol interactions in the Community Earth System Model (CESM) through comparisons with the DOE ARM observations. There are four major goals of the proposed study: (1) Improve the representation of ice microphysical processes in mixed-phase clouds; (2) Develop a long-term multi-sensor mixed-phase cloud dataset; (3) Test the performance of improved ice microphysics in CESM-CAM5 with the ARM data; and (4) Examine mixed-phase cloud microphysics-aerosol-dynamics-radiation interactions in CESM-CAM5. In this project, we have (1) Improved the representation of ice microphysical processes in mixed-phase clouds that include ice nucleation, ice depositional growth through the Wegener–Bergeron–Findeisen (WBF) process, feedbacks between cloud microphysics, dynamics and radiation, and provides links to aerosol properties in the Community Earth System Model (CESM)-Community Atmosphere Model version 5 (CAM5); (2) Developed a long-term multi-sensor mixed-phase cloud dataset. The mixed-phase cloud retrieval algorithms are improved by refining the phase determinations and ice number concentration retrievals. A multi-year mixed-phase cloud observation dataset (1999-2004; October 2013-February 2017) is regenerated at the ARM Barrow site with the improved algorithms. The dataset has been used in the global model evaluation to improve the model parameterizations; (3) Tested the performance of improved ice microphysics in CESM-CAM5 with the ARM data. CESM-CAM5 is run in the DOE Cloud-Associated Parameterizations Testbed (CAPT) and in the single-column model (SCM) mode to facilitate comparison with ARM observations. Multi-year CAPT simulations of seasonal variations of cloud microphysical properties, cloud liquid water path (LWP) and ice water path (IWP), cloud longwave and shortwave forcings, cloud occurrence frequency are evaluated against the ARM multi-sensor mixed-phase cloud retrievals; and (4) Examined mixed-phase cloud microphysics-aerosol-dynamics-radiation interactions in CESM-CAM5 that include the impacts of different ice nucleation mechanisms, sensitivity to dust IN concentration, treatment of the WBF process on mixed-phase cloud properties. Aerosol effect on mixed-phase clouds through the liquid phase (droplet activation) and ice phase processes (e.g., the glaciation indirect effect) is investigated.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRSDate not supplied

Investigation of Cloud Interior Structure Using a Tomographic Technique Based on Radon Transform. Application to the Measurements Made by the Research Scanning Polarimeter During CAMP2Ex

The Research Scanning Polarimeter (RSP) is an airborne along-track scanner measuring the polarized and total reflectances in 9 spectral channels. The RSP's uniquely high angular resolution coupled with the high frequency of measurements allows for characterization of liquid-water cloud droplet sizes using the rainbow structure observed in the polarized reflectance measurements. The RSP observations also provide for derivation of 2D field of extinction coefficient inside the cloud using a tomographic technique. This technique utilizes the family of cloud shapes derived using "cutout" technique and corresponding to a number of thresholds in total reflectance (separating bright cloud from its darker background). These shapes can be interpreted as level curves of an abstract "reflectance density", which is then used for derivation of the directional cloud optical thickness (dCOT) tomogram. The latter is a collection of dCOTs parameterized by the angles and offsets of the corresponding view rays (chords) relative to the cloud center. After this, the inverse Radon Transform (the mathematical basis of the X-ray com-puter tomography) is applied to the dCOT tomogram yielding 2D spatial distribution of the extinction coefficient. The later can be converted into droplet number concentration using the droplet size profiles derived from the RSP's polarized reflectance measurements. After tests on synthetic data this technique was applied to real RSP measurements from NASA's Cloud, Aerosol and Monsoon Processes Philippines Experiment (CAMP2Ex) conducted in the vicinity of the Philippines during the Southwest Monsoon (August–September 2019). We have investigated the interiors of a number of clouds observed during CAMP2Ex focusing on Cu and CuCg (Tcu) cases. Our retrievals were routinely compared with the correlative measurements by lidar (HSRL-2) and cloud radar (APR-3) that were deployed on the same airborne platform (NASA P-3B) during this field experiment.

Research Scanning Polarimeter↗
NASA NTRS2000

The Use of Vegetation For Estimating Broken-Cloud Optical Properties From Surface Measurements

It is known that because of complex three-dimensional (3D) radiative effects of broken clouds, the retrieval of cloud optical properties from upward measurements based on a one-dimensional (1D) inversion technique almost surely fails. To remove radiative effects of 3D cloud structure, we have developed a new technique that retrieves cloud optical thickness for broken clouds above green vegetation from simultaneous surface measurements in the VIS and Near Infrared (NIR) spectral regions. The theoretical basis of the method is the very different spectral behavior of cloud liquid water drops and green vegetation. For example, cloud optical properties, and hence cloud reflectivities, change little between 650 and 860 nm, while the vegetated surface albedo changes from 0.05 to 0.5 between the same two wavelengths. This spectral contrast in surface albedo suggests using ground measurements at both wavelengths not independently, but as an algebraic combination (a spectral index). For a spectral band in the NIR region, the green vegetation acts as a powerful reflector that "illuminates" horizontally inhomogeneous clouds from below. This provides the extra information needed to largely remove the 3D radiative effects, especially in the case of broken clouds; this in turn allows the retrieval of cloud optical depth using traditional 1D radiative transfer theory. This approach is similar to the so-called Green's function problem for radiative transfer where a laser beam illuminates clouds and the resulting "spot-size" of the reflected light around the beam characterizes cloud properties. We generalize Green's function theory to surf ace-cloud interaction and develop new spectral indices from which broken-cloud optical depth can be retrieved.

Marshak, A.↗
NASA NTRS2013

Modeling of 2008 Kasatochi Volcanic Sulfate Direct Radiative Forcing: Assimilation of OMI SO2 Plume Height Data and Comparison with MODIS and CALIOP Observations

Volcanic SO2 column amount and injection height retrieved from the Ozone Monitoring Instrument (OMI) with the Extended Iterative Spectral Fitting (EISF) technique are used to initialize a global chemistry transport model (GEOS-Chem) to simulate the atmospheric transport and lifecycle of volcanic SO2 and sulfate aerosol from the 2008 Kasatochi eruption, and to subsequently estimate the direct shortwave, top-of-the-atmosphere radiative forcing of the volcanic sulfate aerosol. Analysis shows that the integrated use of OMI SO2 plume height in GEOS-Chem yields: (a) good agreement of the temporal evolution of 3-D volcanic sulfate distributions between model simulations and satellite observations from the Moderate Resolution Imaging Spectroradiometer (MODIS) and Cloud-Aerosol Lidar with Orthogonal Polarisation (CALIOP), and (b) an e-folding time for volcanic SO2 that is consistent with OMI measurements, reflecting SO2 oxidation in the upper troposphere and stratosphere is reliably represented in the model. However, a consistent (approx. 25 %) low bias is found in the GEOS-Chem simulated SO2 burden, and is likely due to a high (approx.20 %) bias of cloud liquid water amount (as compared to the MODIS cloud product) and the resultant stronger SO2 oxidation in the GEOS meteorological data during the first week after eruption when part of SO2 underwent aqueous-phase oxidation in clouds. Radiative transfer calculations show that the forcing by Kasatochi volcanic sulfate aerosol becomes negligible 6 months after the eruption, but its global average over the first month is -1.3W/sq m, with the majority of the forcing-influenced region located north of 20degN, and with daily peak values up to -2W/sq m on days 16-17. Sensitivity experiments show that every 2 km decrease of SO2 injection height in the GEOS-Chem simulations will result in a approx.25% decrease in volcanic sulfate forcing; similar sensitivity but opposite sign also holds for a 0.03 m increase of geometric radius of the volcanic aerosol particles. Both sensitivities highlight the need to characterize the SO2 plume height and aerosol particle size from space. While more research efforts are warranted, this study is among the first to assimilate both satellite-based SO2 plume height and amount into a chemical transport model for an improved simulation of volcanic SO2 and sulfate transport.

Wang, J.↗
NASA NTRS1982

Skylab near-infrared observations of clouds indicating supercooled liquid water droplets

Orographically-induced lee-wave clouds were observed over New Mexico by a multichannel scanning radiometer on Skylab during December 1973. Channels centered at 0.83, 1.61 and 2.125 microns were used to determine the cloud optical thickness, thermodynamic phase and effective particle size. An additional channel centered at 11.4 microns was used to determine cloud-top temperature, which was corroborated through comparison with the stereographically determined cloud top altitudes and conventional temperature soundings. Analysis of the measured near-infrared reflection functions at 1.61 and 2.125 microns are most easily interpreted as indicating the presence of liquid-phase water droplets. This interpretation is not conclusive even after considerable effort to understand possible sources for misinterpretation. However, if accepted the resulting phase determination is considered anomalous due to the inferred cloud-top temperatures being in the -32 to -47 C range. Theory for the homogeneous nucleation of pure supercooled liquid water droplets predicts very short lifetimes for the liquid phase at these cold temperatures. A possible explanation for the observations is that the wave-clouds are composed of solution droplets. Impurities in the cloud droplets could decrease the homogeneous freezing rate for these droplets, permitting them to exist for a longer time in the liquid phase, at the cold temperatures found.

Curran, R. J.↗
DOE OSTI2022

Effect of data assimilation in the Polar WRF with 3DVAR on the prediction of radiation, heat flux, cloud, and near surface atmospheric variables over Svalbard

Although the Polar Weather Research and Forecasting (PWRF) model has been developed for polar environments, simulations of atmospheric states in the polar region still have large uncertainties. Therefore, the effects of data assimilation (DA) to improve forecasts in the polar region were investigated for September 2017 using PWRF and the three-dimensional variational (3DVAR) DA method. The experiments without DA and those with DA assimilating only conventional observations and both conventional observations and satellite radiance data were performed. The forecasts from all experiments both without and with DA underestimated (overestimated) the downward longwave (shortwave) radiation flux due to the underestimation of the amount of Arctic clouds. When satellite radiance data (i.e., the Advanced Microwave Sounding Unit-A (AMSU-A) and Microwave Humidity Sounder (MHS)) were assimilated in addition to conventional observations in the PWRF, the distribution and amount of water vapor became closer to observations, which improves cloud liquid water forecasts. Therefore, when both conventional observations and radiance data were assimilated, the 25–30 h forecast errors of the downward longwave and shortwave radiation fluxes and sensible and latent heat fluxes decreased by 12.7%, 8.1%, 3.2%, and 7.8% with the WSM5 scheme and by 17.1%, 4.7%, 2.5%, and 3.1% with the 2-moment Morrison scheme, respectively, compared to those in the experiments without DA. The forecast errors of the 10 m wind and 2 m temperature with DA were smaller than those without DA at most observation stations. Therefore, the uncertainties of the Arctic forecasts in the PWRF decreased when using DA. To further improve Arctic forecasts, the assimilation of various additional satellite data is necessary.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Understanding aerosol–cloud interactions using a single-column model for a cold-air outbreak case during the ACTIVATE campaign

Marine boundary layer clouds play a critical role in Earth's energy balance. Their microphysical and radiative properties are highly impacted by ambient aerosols and dynamic forcings. In this study, we evaluate the representation of these clouds and related aerosol–cloud interaction processes in the single-column version of the E3SM climate model (SCM) against field measurements collected during the NASA ACTIVATE campaign over the western North Atlantic, as well as intercompare results with high-resolution process level models. We show that E3SM SCM reproduces the macrophysical properties of post-frontal boundary layer clouds in a cold-air outbreak (CAO) case well. However, it generates fewer but larger cloud droplets compared to aircraft measurements. Further sensitivity tests show that the underestimation of both aerosol number concentration and vertical velocity variance contributes to this bias. Aerosol–cloud interactions are examined by perturbing prescribed aerosol properties in E3SM SCM with fixed dynamics. Higher aerosol number concentration or hygroscopicity leads to more numerous but smaller cloud droplets, resulting in a stronger cooling via shortwave cloud forcing. This apparent Twomey effect is consistent with prior climate model studies. The cloud liquid water path shows a weakly positive relation with cloud droplet number concentration due to precipitation suppression. This weak aerosol effect on cloud macrophysics may be attributed to the dominant impact of strong dynamical forcing associated with the CAO. Our findings indicate that the SCM framework is a key tool to bridge the gap between climate models, process level models, and field observations to facilitate process level understanding.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Diurnal evolution of non-precipitating marine stratocumuli in a large-eddy simulation ensemble

Abstract. We explore the cloud system evolution of non-precipitating marine stratocumuli with a focus on the impacts of the diurnal cycle and free-tropospheric (FT) humidity based on an ensemble of 244 large-eddy simulations generated by perturbing initial thermodynamic profiles and aerosol conditions. Cases are categorized based on their degree of decoupling and the cloud liquid water path (LWPc, based on model columns with cloud optical depths greater than one). A budget analysis method is proposed to analyze the evolution of cloud water in both coupled and decoupled boundary layers. More coupled clouds start with a relatively low LWPc and cloud fraction (fc) but experience the least decrease in LWPc and fc during the daytime. More decoupled clouds undergo greater daytime reduction in LWPc and fc, especially those with higher LWPc at sunrise because they suffer from faster weakening of net radiative cooling. During the nighttime, a positive correlation between FT humidity and the LWPc emerges, consistent with higher FT humidity reducing both radiative cooling and the humidity jump, both of which reduce entrainment and increase LWPc. The LWPc is more likely to decrease during the nighttime for a larger LWPc and greater inversion base height (zi), conditions under which entrainment dominates as turbulence develops. In the morning, the rate of the LWPc reduction depends on the LWPc at sunrise, zi, and the degree of decoupling, with distinct contributions from subsidence and radiation.

Chen, Yao-Sheng (ORCID:0000000208354132)↗
NASA NTRS1984

Stratocumulus cloud field reflected fluxes - The effect of cloud shape

The reflected fluxes of stratocumulus cloud fields are calculated as a function of sky cover aspect ratio and cloud shape. In order to obtain a better fit with general circulation models (GCMs), cloud liquid water volume values were kept invariant relative to cloud shape. On the basis of the required accuracy of the Earth Radiation Budget Experiment (ERBE), an order of magnitude value of 10 W per sq m was used to estimate the difference between plane-parallel and broken cloudiness reflected fluxes. An empirical relationship for effective cloud cover at a solar zenith angle of 60 deg is derived. The relationship allows for the accurate computation of broken cloud field reflected fluxes using plane-parallel calculations. It is predicted that more accurate estimates of broken cloud field radiative properties may be possible in the future.

Welch, R. M.↗
NASA NTRS2005

A Climatology of Midlatitude Continental Clouds from the ARM SGP Site: Low-Level Cloud Macrophysical, Microphysical, and Radiative Properties - Part I

A record of single-layer and overcast low cloud (stratus) properties has been generated using approximately 4000 hours of data collected from January 1997 to December 2002 at the Atmospheric Radiation Measurement (ARM) Southern Great Plains Central Facility (SCF). The cloud properties include liquid-phase and liquid-dominant, mixed-phase, low cloud macrophysical, microphysical, and radiative properties including cloud-base and -top heights and temperatures, and cloud physical thickness derived from a ground-based radar and lidar pair, and rawinsonde sounding; cloud liquid water path (LWP) and content (LWC), and cloud-droplet effective radius (r(sub e)) and number concentration (N) derived from the macrophysical properties and radiometer data; and cloud optical depth (tau), effective solar transmission (gamma), and cloud/top-of-atmosphere albedos (R(sub cldy)/R(sub TOA)) derived from Eppley precision spectral pyranometer measurements. The cloud properties were analyzed in terms of their seasonal, monthly, and hourly variations. In general, more stratus clouds occur during winter and spring than in summer. Cloud-layer altitudes and physical thicknesses were higher and greater in summer than in winter with averaged physical thicknesses of 0.85 km and 0.73 km for day and night, respectively. The seasonal variations of LWP, LWC, N. tau, R(sub cldy), and R(sub TOA) basically follow the same pattern with maxima and minima during winter and summer, respectively. There is no significant variation in mean r(sub e), however, despite a summertime peak in aerosol loading, Although a considerable degree of variability exists, the 6-yr average values of LWP, LWC, r(sub e), N, tau, gamma, R(sub cldy) and R(sub TOA) are 150 gm(exp -2) (138), 0.245 gm(exp -3) (0.268), 8.7 micrometers (8.5), 213 cm(exp -3) (238), 26.8 (24.8), 0.331, 0.672, 0.563 for daytime (nighttime). A new conceptual model of midlatitude continental low clouds at the ARM SGP site has been developed from this study. The low stratus cloud amount monotonically increases from midnight to early morning (0930 LT), and remains large until around local noon, then declines until 1930 LT when it levels off for the remainder of the night. In the morning, the stratus cloud layer is low, warm, and thick with less LWC, while in the afternoon it is high, cold, and thin with more LWC. Future parts of this series will consider other cloud types and cloud radiative forcing at the ARM SCF.

Dong, Xiquan↗
NASA NTRS2024

Long-Term Trends in Aerosols, Low Clouds, and Large-scale Meteorology over the Western North Atlantic from 2003 to 2020

A continuous decrease of aerosol over the western North Atlantic Ocean (WNAO) on decadal timescales provides a long-term experiment to evaluate how other natural and anthropogenic processes affect the manifestation of aerosol-cloud interactions in this region. Furthermore, the WNAO is a natural laboratory with diverse aerosol sources, marine boundary layer clouds that are more variable than marine stratocumulus deck regions, and unique flow regimes set up by the Gulf Stream and semi-permanent Bermuda High. We investigate how satellite-retrieved macrophysical and microphysical properties of low clouds and the surface shortwave irradiance changed from 2003 to 2020, in tandem with this aerosol decrease. The decadal changes in large-scale meteorology relating to the North Atlantic Oscillation (NAO) are also examined. We find no significant changes in low-cloud fraction but a widespread reduction in low-cloud optical depth attributed to fewer and larger cloud droplets with almost no change in cloud liquid water path. Despite robust signals in low-cloud optical properties together with aerosol decrease, a corresponding increase in the surface shortwave irradiance trends, also called surface brightening, is lacking. This absence of brightening is potentially due to concomitant changes found in large-scale meteorology associated with NAO— a Bermuda High strengthening, sea surface warming, and atmospheric moistening— as well as an increase in high cloud fraction that can counteract the surface brightening. Ultimately, our findings suggest that spatial patterns in the decadal meteorological variability, likely set up by NAO, contribute more to the surface cloud radiative effect over the WNAO than aerosol-cloud interactions.

J Minnie Park↗
NASA NTRS1990

Characterization of supercooled liquid water in cirrus clouds from FIRE ETO lidar observations

The various modes of occurrence of supercooled liquid water in cirrus clouds are discussed using the data from the FIRE extended time observations (ETO). Results from lidar observations show that cirrus cloud scenes viewed from satellites may contain mixtures of 'high' and 'middle' cloud varieties, which affect the assessment of the derived cirrus cloud properties.

Sassen, Kenneth↗
DOE OSTI2023

Insights into the relation between vertical cloud structure and dynamics of three polar lows: Observations from COMBLE

The vertical structure of three polar lows is described using profiling radar, lidar, and passive remote sensors deployed at a coastal site in northern Norway. The data were collected as part of the Cold-air Outbreaks in the Marine Boundary Layer Experiment (COMBLE). These data are examined in the context of satellite imagery, operational weather radar reflectivity imagery, and output from the AROME-Arctic model. A comparison to satellite images shows that AROME-Arctic captured the polar lows well. All three polar lows form in marine cold-air outbreaks and are surrounded by open-cellular convection typical of such outbreaks. Two of the lows form in a forward shear environment, and one under reverse shear. Initially, the three polar lows are comma-shaped; two of them transition to be more spirali-form at their mature stage and have mostly cloud-free warm cores. The warm cores are the result of a warm-seclusion process. All three lows have stratiform precipitation bands, marked by little cloud liquid water, and rather high surface precipitation rate. The vertical drafts and turbulence in these stratiform clouds are generally weak. In conclusion, all three lows also have convective clouds, which have stronger vertical drafts, stronger turbulence, and pockets of high liquid water content.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2017

Strong Constraints on Aerosol-Cloud Interactions from Volcanic Eruptions

Aerosols have a potentially large effect on climate, particularly through their interactions with clouds, but the magnitude of this effect is highly uncertain. Large volcanic eruptions produce sulfur dioxide, which in turn produces aerosols; these eruptions thus represent a natural experiment through which to quantify aerosol-cloud interactions. Here we show that the massive 2014-2015 fissure eruption in Holuhraun, Iceland, reduced the size of liquid cloud droplets - consistent with expectations - but had no discernible effect on other cloud properties. The reduction in droplet size led to cloud brightening and global-mean radiative forcing of around minus 0.2 watts per square metre for September to October 2014. Changes in cloud amount or cloud liquid water path, however, were undetectable, indicating that these indirect effects, and cloud systems in general, are well buffered against aerosol changes. This result will reduce uncertainties in future climate projections, because we are now able to reject results from climate models with an excessive liquid-water-path response.

atmospheric science↗
NASA NTRS2015

An Assessment of the SEA Multi-Element Sensor for Liquid Water Content Calibration of the NASA GRC Icing Research Tunnel

The NASA Glenn Icing Research tunnel has been using an Icing Blade technique to measure cloud liquid water content (LWC) since 1980. The IRT conducted tests with SEA Multi-Element sensors from 2009 to 2011 to assess their performance in measuring LWC. These tests revealed that the Multi-Element sensors showed some significant advantages over the Icing Blade, particularly at higher water contents, higher impingement rates, and large drop sizes. Results of these and other tests are presented here.

multi-wire↗
NASA NTRS1983

Laboratory and field observations related to ice particle and aircraft charging in convective storms

Graupel particle charging in simulated cloud conditions which show the need for the presence of ice crystals and cloud water simultaneously except under conditions where secondary ice crystal production occurs when charging initially occurs in the absence of ice crystals was examined. The magnitude of the charging increases with size of ice crystals, and impact velocity; it is also sensitive to impurities. The magnitude of the charge is also sensitive to temperature and the sign changes between -10 and -20 C, depending on cloud liquid water content. Aircraft studies were carried out in Montana convective clouds to test the validity of the extrapolation of the laboratory data to the atmosphere from the viewpoint of generation of charge, electric field, and aircraft charging during cloud penetration.

Christian, H.↗
NASA NTRS1991

A surface-based cloud observing system

The paper describes a surface-based system, called the Cloud Observing System (COS), that was developed for measurements of the dynamical and thermodynamical properties of clouds and of their interaction with the large-scale environment, by combining several remote sensors and in situ systems. The atmospheric parameters that will be measured by COS include precipitation, the velocity and direction of wind, the cloud liquid water, the low-level winds and turbulence structure, integrated liquid and vapor quantities, the temperature and water profiles, the cloud radiance and the cloud base temperature, irradiances at the surface, the low-level temperature profile, the cloud-base height, and the cloud fraction; video cameras will provide visual records of clouds.

Albrecht, B. A.↗
NASA NTRS2016

Validation of Cloud Parameters Derived from Geostationary Satellites, AVHRR, MODIS, and VIIRS Using SatCORPS Algorithms

Validation is a key component of remote sensing that can take many different forms. The NASA LaRC Satellite ClOud and Radiative Property retrieval System (SatCORPS) is applied to many different imager datasets including those from the geostationary satellites, Meteosat, Himiwari-8, INSAT-3D, GOES, and MTSAT, as well as from the low-Earth orbiting satellite imagers, MODIS, AVHRR, and VIIRS. While each of these imagers have similar sets of channels with wavelengths near 0.65, 3.7, 11, and 12 micrometers, many differences among them can lead to discrepancies in the retrievals. These differences include spatial resolution, spectral response functions, viewing conditions, and calibrations, among others. Even when analyzed with nearly identical algorithms, it is necessary, because of those discrepancies, to validate the results from each imager separately in order to assess the uncertainties in the individual parameters. This paper presents comparisons of various SatCORPS-retrieved cloud parameters with independent measurements and retrievals from a variety of instruments. These include surface and space-based lidar and radar data from CALIPSO and CloudSat, respectively, to assess the cloud fraction, height, base, optical depth, and ice water path; satellite and surface microwave radiometers to evaluate cloud liquid water path; surface-based radiometers to evaluate optical depth and effective particle size; and airborne in-situ data to evaluate ice water content, effective particle size, and other parameters. The results of comparisons are compared and contrasted and the factors influencing the differences are discussed.

Minnis, P.↗