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Earth atmosphere radiation fields analysis from Nimbus 3 five-channel scanning radiometer measurements, determining mean planetary albedo and temperature
The study, in addition to investigating the consistency of climatological products from Nimbus-7 Earth Radiation Budget and Temperature Humidity Infrared Radiometer experiments, focussed on the climatological analysis of the specified regions of the Earth. The climatological study consisted of the effects of various types of clouds on the net radiation, albedos, and emitted radiation. In addition to a correlational study for determining consistency level of data, a population study of the regions was formulated and conducted. The regions under this study were formed by clustering the target areas using the criteria of climatological conditions such as geography, ocean, and land. Research is limited to tropics from 18 deg north to 18 deg south. A correlational study indicates that there is high positive correlation between high clouds and albedo, and a reduced negative correlation between albedo and net radiation.
The ERBE-like Monthly Geographical Averages (ES-4) product contains a month of space and time averaged Clouds and the Earth's Radiant Energy System (CERES) data for a single scanner instrument. The ES-4 is also produced for combinations of scanner instruments. For each observed 2.5-degree spatial region, the daily average, the hourly average over the month, and the overall monthly average of shortwave and longwave fluxes at the Top-of-the-Atmosphere (TOA) from the CERES ES-9 product are spatially nested up from 2.5-degree regions to 5- and 10-degree regions, to 2.5-, 5-, and 10-degree zonal averages, and to global monthly averages. For each nested area, the albedo and net flux are given. For each region, the daily average flux is estimated from an algorithm that uses the available hourly data, scene identification data, and diurnal models. This algorithm is 'like' the algorithm used for the Earth Radiation Budget Experiment (ERBE). The following CERES ES4 data sets are currently available: CER_ES4_FM1+FM2_Edition1 CER_ES4_PFM+FM1+FM2_Edition1 CER_ES4_PFM+FM1+FM2_Edition2 CER_ES4_PFM+FM1_Edition1 CER_ES4_PFM+FM2_Edition1 CER_ES4_TRMM-PFM_Edition1 CER_ES4_TRMM-PFM_Edition2 CER_ES4_Terra-FM1_Edition1 CER_ES4_Terra-FM2_Edition1 CER_ES4_FM1+FM2_Edition2 CER_ES4_Terra-FM1_Edition2 CER_ES4_Terra-FM2_Edition2 CER_ES4_Aqua-FM3_Edition1 CER_ES4_Aqua-FM4_Edition1 CER_ES4_FM1+FM2+FM3+FM4_Edition1 CER_ES4_Aqua-FM3_Edition2 CER_ES4_Aqua-FM4_Edition2 CER_ES4_FM1+FM3_Edition2 CER_ES4_FM1+FM4_Edition2 CER_ES4_PFM+FM1_Edition2 CER_ES4_PFM+FM2_Edition2 CER_ES4_Aqua-FM3_Edition1-CV CER_ES4_Aqua-FM4_Edition1-CV CER_ES4_Terra-FM1_Edition1-CV CER_ES4_Terra-FM2_Edition1-CV. [Location=GLOBAL] [Temporal_Coverage: Start_Date=1998-01-01; Stop_Date=2000-03-31] [Spatial_Coverage: Southernmost_Latitude=-90; Northernmost_Latitude=90; Westernmost_Longitude=-180; Easternmost_Longitude=180] [Data_Resolution: Latitude_Resolution=2.5 degree; Longitude_Resolution=2.5 degree; Horizontal_Resolution_Range=250 km - < 500 km or approximately 2.5 degrees - < 5.0 degrees; Temporal_Resolution=1 month; Temporal_Resolution_Range=Monthly - < Annual].
The ERBE-like Monthly Regional Averages (ES-9) product contains a month of space and time averaged Clouds and the Earth's Radiant Energy System (CERES) data for a single scanner instrument. The ES-9 is also produced for combinations of scanner instruments. All instantaneous shortwave and longwave fluxes at the Top-of-the-Atmosphere (TOA) from the CERES ES-8 product for a month are sorted by 2.5-degree spatial regions, by day number, and by the local hour of observation. The mean of the instantaneous fluxes for a given region-day-hour bin is determined and recorded on the ES-9 along with other flux statistics and scene information. For each region, the daily average flux is estimated from an algorithm that uses the available hourly data, scene identification data, and diurnal models. This algorithm is 'like' the algorithm used for the Earth Radiation Budget Experiment (ERBE). The ES-9 also contains hourly average fluxes for the month and an overall monthly average for each region. These average fluxes are given for both clear-sky and total-sky scenes. The following CERES ES9 data sets are currently available: CER_ES9_FM1+FM2_Edition1 CER_ES9_PFM+FM1+FM2_Edition1 CER_ES9_PFM+FM1+FM2_Edition2 CER_ES9_PFM+FM1_Edition1 CER_ES9_PFM+FM2_Edition1 CER_ES9_PFM+FM1_Edition2 CER_ES9_PFM+FM2_Edition2 CER_ES9_TRMM-PFM_Edition1 CER_ES9_TRMM-PFM_Edition2 CER_ES9_Terra-FM1_Edition1 CER_ES9_Terra-FM2_Edition1 CER_ES9_FM1+FM2_Edition2 CER_ES9_Terra-FM1_Edition2 CER_ES9_Terra-FM2_Edition2 CER_ES9_Aqua-FM3_Edition1 CER_ES9_Aqua-FM4_Edition1 CER_ES9_FM1+FM2+FM3+FM4_Edition1 CER_ES9_Aqua-FM3_Edition2 CER_ES9_Aqua-FM4_Edition2 CER_ES9_FM1+FM3_Edition2 CER_ES9_FM1+FM4_Edition2 CER_ES9_Aqua-FM3_Edition1-CV CER_ES9_Aqua-FM4_Edition1-CV CER_ES9_Terra-FM1_Edition1-CV CER_ES9_Terra-FM2_Edition1-CV. [Location=GLOBAL] [Temporal_Coverage: Start_Date=1998-01-01; Stop_Date=2005-12-31] [Spatial_Coverage: Southernmost_Latitude=-90; Northernmost_Latitude=90; Westernmost_Longitude=-180; Easternmost_Longitude=180] [Data_Resolution: Latitude_Resolution=2.5 degree; Longitude_Resolution=2.5 degree; Horizontal_Resolution_Range=250 km - < 500 km or approximately 2.5 degrees - < 5.0 degrees; Temporal_Resolution=hourly, daily, monthly; Temporal_Resolution_Range=Hourly - < Daily, Daily - < Weekly, Monthly - < Annual].
The ERBE-like Monthly Regional Averages (ES-9) product contains a month of space and time averaged Clouds and the Earth's Radiant Energy System (CERES) data for a single scanner instrument. The ES-9 is also produced for combinations of scanner instruments. All instantaneous shortwave and longwave fluxes at the Top-of-the-Atmosphere (TOA) from the CERES ES-8 product for a month are sorted by 2.5-degree spatial regions, by day number, and by the local hour of observation. The mean of the instantaneous fluxes for a given region-day-hour bin is determined and recorded on the ES-9 along with other flux statistics and scene information. For each region, the daily average flux is estimated from an algorithm that uses the available hourly data, scene identification data, and diurnal models. This algorithm is 'like' the algorithm used for the Earth Radiation Budget Experiment (ERBE). The ES-9 also contains hourly average fluxes for the month and an overall monthly average for each region. These average fluxes are given for both clear-sky and total-sky scenes. The following CERES ES9 data sets are currently available: CER_ES9_FM1+FM2_Edition1 CER_ES9_PFM+FM1+FM2_Edition1 CER_ES9_PFM+FM1+FM2_Edition2 CER_ES9_PFM+FM1_Edition1 CER_ES9_PFM+FM2_Edition1 CER_ES9_PFM+FM1_Edition2 CER_ES9_PFM+FM2_Edition2 CER_ES9_TRMM-PFM_Edition1 CER_ES9_TRMM-PFM_Edition2 CER_ES9_Terra-FM1_Edition1 CER_ES9_Terra-FM2_Edition1 CER_ES9_FM1+FM2_Edition2 CER_ES9_Terra-FM1_Edition2 CER_ES9_Terra-FM2_Edition2 CER_ES9_Aqua-FM3_Edition1 CER_ES9_Aqua-FM4_Edition1 CER_ES9_FM1+FM2+FM3+FM4_Edition1 CER_ES9_Aqua-FM3_Edition2 CER_ES9_Aqua-FM4_Edition2 CER_ES9_FM1+FM3_Edition2 CER_ES9_FM1+FM4_Edition2 CER_ES9_Aqua-FM3_Edition1-CV CER_ES9_Aqua-FM4_Edition1-CV CER_ES9_Terra-FM1_Edition1-CV CER_ES9_Terra-FM2_Edition1-CV. [Location=GLOBAL] [Temporal_Coverage: Start_Date=1998-01-01; Stop_Date=2005-03-29] [Spatial_Coverage: Southernmost_Latitude=-90; Northernmost_Latitude=90; Westernmost_Longitude=-180; Easternmost_Longitude=180] [Data_Resolution: Latitude_Resolution=2.5 degree; Longitude_Resolution=2.5 degree; Horizontal_Resolution_Range=250 km - < 500 km or approximately 2.5 degrees - < 5.0 degrees; Temporal_Resolution=hourly, daily, monthly; Temporal_Resolution_Range=Hourly - < Daily, Daily - < Weekly, Monthly - < Annual].
NASA’S Origins, Spectral Interpretation, Resource Identification and Security-Regolith Explorer (OSIRIS-REx) spacecraft recently arrived at the near-Earth asteroid (101955) Bennu, a primitive body that represents the objects that may have brought prebiotic molecules and volatiles such as water to Earth1. Bennu is a low-albedo B-type asteroid2 that has been linked to organic-rich hydrated carbonaceous chondrites3. Such meteorites are altered by ejection from their parent body and contaminated by atmospheric entry and terrestrial microbes. Therefore, the primary mission objective is to return a sample of Bennu to Earth that is pristine—that is, not affected by these processes4. The OSIRIS-REx spacecraft carries a sophisticated suite of instruments to characterize Bennu’s global properties, support the selection of a sampling site and document that site at a sub-centimetre scale5,6,7,8,9,10,11. Here we consider early OSIRIS-REx observations of Bennu to understand how the asteroid’s properties compare to pre-encounter expectations and to assess the prospects for sample return. The bulk composition of Bennu appears to be hydrated and volatile-rich, as expected. However, in contrast to pre-encounter modelling of Bennu’s thermal inertia12 and radar polarization ratios13—which indicated a generally smooth surface covered by centimetre-scale particles—resolved imaging reveals an unexpected surficial diversity. The albedo, texture, particle size and roughness are beyond the spacecraft design specifications. On the basis of our pre-encounter knowledge, we developed a sampling strategy to target 50-metre-diameter patches of loose regolith with grain sizes smaller than two centimetres4. We observe only a small number of apparently hazard-free regions, of the order of 5 to 20 metres in extent, the sampling of which poses a substantial challenge to mission success.
The idea of a habitable Venus epoch has gained traction in recent years via 1-D and 3-D General Circulation Modeling (GCM) efforts [1,2,3]. Although recent work has supported an alternative permanent hot and dry scenario [4]. However, the habitable scenario presents us with a conundrum - how does a terrestrial planet transform from temperate to hot-house? For decades it was proposed that the gradual brightening of the sun was the probable cause [5]. Yet 4 billion years ago Venus was receiving nearly 1.4 times the insolation that Earth receives today, and many studies have put Earth at the inner boundary of the habitable zone today [6]. The newer 3-D GCM efforts have demonstrated that if Venus had an early habitable period, that the cloud-albedo feedback responsible for maintaining temperate surface conditions [7] could still be in operation today. From this perspective increasing insolation through time cannot be an answer to the transition from habitable to hot-house. We propose that the 'Great Climate Transition' (GCT) was trigged by simultaneous large igneous provinces (LIPs) akin to those like the Siberian Traps responsible for the End Permian [8]. We have taken the most up to date LIP database for Earth [9] and characterized their distribution through time as random or nearly random. Next we initiate a large suite of Monte Carlo simulations based on this record and generate the likelihood for simultaneous, or environmentally overlapping events in this hypothetical setup. We find the probability of such events to be quite high, a probable cause for Venus' GCT, and a possible harbinger of things to come for Earth.
Seventy-two images of the S-class asteroid 5535 Annefrank, acquired on 2 November 2002 at target ranges of 11,415??8.5 km, were transmitted to Earth as a part of an engineering readiness test of the Stardust mission. Forty-four of these were used to create a phase curve extending to 134, the largest angle yet achieved for any S-class asteroid. Flux fell by more than six magnitudes between the extrapolated 0 and 134. A maximum illuminated cross section of 16 km2 was seen at a phase angle of 47.2. Assuming a camera efficiency of 75%, a broadband (470?? nm) geometric albedo of 0.24 was derived for Annefrank.
The behavior of Mars as observed by the Viking infrared thermal mapper (IRTM) is considered. The IRTM is a 28-channel, 4-telescope radiometer that operated in six spectral bands. The studies considered include observations from the interplanetary phase through data collection on November 7, 1976. During this interval, thermal mapping of the whole Martian surface has been possible. Attention is given to polar temperatures, global albedos, predawn temperatures, a thermal inertia contour map, geometry considerations, clouds, aspects of predawn warming, and observations of earth.
The implementation of the Climate Absolute Radiance and Refractivity Observatory (CLARREO) mission was recommended by the National Research Council in 2007 to provide an on-orbit intercalibration standard with accuracy of 0.3% (k = 2) for relevant Earth observing sensors. The goal of reference intercalibration, as established in the Decadal Survey, is to enable rigorous high-accuracy observations of critical climate change parameters, including reflected broadband radiation [Clouds and Earth's Radiant Energy System (CERES)], cloud properties [Visible Infrared Imaging Radiometer Suite (VIIRS)], and changes in surface albedo, including snow and ice albedo feedback. In this paper, we describe the CLARREO approach for performing intercalibration on orbit in the reflected solar (RS) wavelength domain. It is based on providing highly accurate spectral reflectance and reflected radiance measurements from the CLARREO Reflected Solar Spectrometer (RSS) to establish an on-orbit reference for existing sensors, namely, CERES and VIIRS on Joint Polar Satellite System satellites, Advanced Very High Resolution Radiometer and follow-on imagers on MetOp, Landsat imagers, and imagers on geostationary platforms. One of two fundamental CLARREO mission goals is to provide sufficient sampling of high-accuracy observations that are matched in time, space, and viewing angles with measurements made by existing instruments, to a degree that overcomes the random error sources from imperfect data matching and instrument noise. The data matching is achieved through CLARREO RSS pointing operations on orbit that align its line of sight with the intercalibrated sensor. These operations must be planned in advance; therefore, intercalibration events must be predicted by orbital modeling. If two competing opportunities are identified, one target sensor must be given priority over the other. The intercalibration method is to monitor changes in targeted sensor response function parameters: effective offset, gain, nonlinearity, optics spectral response, and sensitivity to polarization. In this paper, we use existing satellite data and orbital simulationmethods to determinemission requirements for CLARREO, its instrument pointing ability, methodology, and needed intercalibration sampling and data matching for accurate intercalibration of RS radiation sensors on orbit.
Background and Objective: The surface temperature of the Arctic is projected to warm more than any other region on Earth (i.e., Arctic Amplification). Even though the increase of solar absorption, due to the reduction of the surface albedo associated with the loss of sea ice, is strongest in summer, the warming is largest in late fall/early winter and smallest in summer. The most common theory put forward to explain the suppressed summer warming is that most of the additional solar energy goes into the melting of sea ice. The energy gain in summer, however, is thought to lead to the Arctic warming maximum in late fall/early winter by leading to enhanced heat release during this time period as a result of the enhanced surface latent and sensible heat fluxes into the atmosphere, also a consequence of the loss and thinning of sea-ice, warming the surface air temperature. While this commonly accepted theory makes clear the importance of sea-ice loss on Arctic warming, by focusing on surface skin temperature our study proposes a differing perspective on how sea-ice decline amplifies Arctic warming and establishes its seasonal pattern.
Ice sheet surface conditions and their subsequent impact on surface mass balance play an important role in ice sheet dynamics and ice sheet interaction with the overlying atmosphere and surrounding ocean. The NASA Global Modeling and Assimilation Office’s (GMAO) Goddard Earth Observing System (GEOS) ecosystem of models and reanalyses model ice sheet and glacier surface mass balance with a moderately complex snow and ice module, including prognostic surface albedo evolution, fractional snow cover, and snowpack hydrology and meltwater retention. With this configuration, Greenland near surface air temperatures and ice sheet melt are well represented in MERRA-2, GMAO’s current atmospheric reanalysis; however, the similarity to observations in some regions is due, in part, to compensating biases in surface energy budget. Recent improvements to GEOS’ cloud microphysics and longwave radiation parameterizations reduced biases in surface net longwave radiation and exacerbated surface net shortwave radiation biases, effectively increasing near surface temperatures and melting, particularly during the summer months. Here, we demonstrate the Earth system response to an improved representation of the ice sheet surface focused on minimizing the surface energy biases and increasing spatial and temporal representativeness. New changes to the surface albedo parameterization, including the introduction of a prognostic aerosol darkening scheme, help mitigate shortwave biases, while modifications to surface roughness characteristics improve near surface sensible heat fluxes. Focusing on the Arctic and Greenland, we examine the combined impact on these changes on regional weather conditions and ice sheet surface mass balance using a high resolution atmospheric only experiment, and we use a coupled model configuration to assess the impact on oceanic conditions and subseasonal-to-seasonal prediction. Overall, these improvements increase modeled ice sheet surface realism and provide a strong basis for more accurate ice sheet mass balance in GMAO’s future reanalyses and forecasting systems.
Ice sheet surface conditions and their subsequent impact on surface mass balance play an important role in ice sheet dynamics and ice sheet interaction with the overlying atmosphere and surrounding ocean. The NASA Global Modeling and Assimilation Office’s (GMAO) Goddard Earth Observing System (GEOS) ecosystem of models and reanalyses model ice sheet and glacier surface mass balance with a moderately complex snow and ice module, including prognostic surface albedo evolution, fractional snow cover, and snowpack hydrology and meltwater retention. With this configuration, Greenland near surface air temperatures and ice sheet melt are well represented in MERRA-2, GMAO’s current atmospheric reanalysis; however, the similarity to observations in some regions is due, in part, to compensating biases in surface energy budget. Recent improvements to GEOS’ cloud microphysics and longwave radiation parameterizations reduced biases in surface net longwave radiation and exacerbated surface net shortwave radiation biases, effectively increasing near surface temperatures and melting, particularly during the summer months. Here, we demonstrate the Earth system response to an improved representation of the ice sheet surface focused on minimizing the surface energy biases and increasing spatial and temporal representativeness. New changes to the surface albedo parameterization, including the introduction of a prognostic aerosol darkening scheme, help mitigate shortwave biases, while modifications to surface roughness characteristics improve near surface sensible heat fluxes. Focusing on the Arctic and Greenland, we examine the combined impact on these changes on regional weather conditions and ice sheet surface mass balance using a high resolution atmospheric only experiment, and we use a coupled model configuration to assess the impact on oceanic conditions and subseasonal-to-seasonal prediction. Overall, these improvements increase modeled ice sheet surface realism and provide a strong basis for more accurate ice sheet mass balance in GMAO’s future reanalyses and forecasting systems.
The ERBE-like Monthly Geographical Averages (ES-4) product contains a month of space and time averaged Clouds and the Earth's Radiant Energy System (CERES) data for a single scanner instrument. The ES-4 is also produced for combinations of scanner instruments. For each observed 2.5-degree spatial region, the daily average, the hourly average over the month, and the overall monthly average of shortwave and longwave fluxes at the Top-of-the-Atmosphere (TOA) from the CERES ES-9 product are spatially nested up from 2.5-degree regions to 5- and 10-degree regions, to 2.5-, 5-, and 10-degree zonal averages, and to global monthly averages. For each nested area, the albedo and net flux are given. For each region, the daily average flux is estimated from an algorithm that uses the available hourly data, scene identification data, and diurnal models. This algorithm is 'like' the algorithm used for the Earth Radiation Budget Experiment (ERBE). The following CERES ES4 data sets are currently available: CER_ES4_FM1+FM2_Edition1 CER_ES4_PFM+FM1+FM2_Edition1 CER_ES4_PFM+FM1+FM2_Edition2 CER_ES4_PFM+FM1_Edition1 CER_ES4_PFM+FM2_Edition1 CER_ES4_TRMM-PFM_Edition1 CER_ES4_TRMM-PFM_Edition2 CER_ES4_Terra-FM1_Edition1 CER_ES4_Terra-FM2_Edition1 CER_ES4_FM1+FM2_Edition2 CER_ES4_Terra-FM1_Edition2 CER_ES4_Terra-FM2_Edition2 CER_ES4_Aqua-FM3_Edition1 CER_ES4_Aqua-FM4_Edition1 CER_ES4_FM1+FM2+FM3+FM4_Edition1 CER_ES4_Aqua-FM3_Edition2 CER_ES4_Aqua-FM4_Edition2 CER_ES4_FM1+FM3_Edition2 CER_ES4_FM1+FM4_Edition2 CER_ES4_PFM+FM1_Edition2 CER_ES4_PFM+FM2_Edition2 CER_ES4_Aqua-FM3_Edition1-CV CER_ES4_Aqua-FM4_Edition1-CV CER_ES4_Terra-FM1_Edition1-CV CER_ES4_Terra-FM2_Edition1-CV. [Location=GLOBAL] [Temporal_Coverage: Start_Date=1998-01-01; Stop_Date=2000-03-31] [Spatial_Coverage: Southernmost_Latitude=-90; Northernmost_Latitude=90; Westernmost_Longitude=-180; Easternmost_Longitude=180] [Data_Resolution: Latitude_Resolution=2.5 degree; Longitude_Resolution=2.5 degree; Horizontal_Resolution_Range=250 km - < 500 km or approximately 2.5 degrees - < 5.0 degrees; Temporal_Resolution=1 month; Temporal_Resolution_Range=Monthly - < Annual].
Impacts between asteroid-sized objects have dominated the solar system's history and played a significant role in forming asteroid families. The New Polana family is a low-inclination and the most prominent low-albedo family within the inner Main Belt between the v6 secular resonance at ~2.0 AU and the 3:1 mean-motion resonance with Jupiter at ~2.5 AU [1]. This family formed over 2000 Myr ago and is parented by the B-type asteroid (142) Polana [1]. [2] and [3] found that primitive near-Earth asteroids (NEAs), including Hayabusa2’s asteroid target (162173) Ryugu and OSIRIS-REx’s asteroid target (101955) Bennu, are likely disrupted fragments that originated during the formation of the New Polana family. Other possible sources of primitive NEAs in the inner Main Belt include the Clarissa, Erigone, Polana, and Sulamitis, families and the collisionally evolved background asteroids outside these families [2, 4]. The age of the solar system is longer than the collisional lifetime of asteroid Bennu [5], a rubble pile asteroid with a mean diameter of 490.06 ± 0.16 m [6] and a spinning top-like shape [7]. Asteroid 142 Polana, the largest remnant of the New Polana family [1], has been spectrally (~0.5-2.5 µm) and dynamically linked to asteroid Bennu [e.g., 2]. Bennu’s spectra were measured over the wavelength range from 0.4 to 4.3 µm with OSIRIS-REx Visible and InfraRed Spectrometer (OVIRS) [8]. Here, we investigate the compositional linkage of asteroids Polana and Bennu using 3-µm Polana spectra measured at the Infrared Telescope Facility (IRTF)
Aerosols affect climate through direct and indirect effects. The direct effect of aerosols (e.g., sulfates) includes reflection of sunlight back toward space and for some aerosols (e.g., smoke particles), absorption in the atmosphere; both effects cool the Earth's surface. The indirect effect of aerosols refers to the modification of cloud microphysical properties, thereby affecting the radiation balance. Higher concentrations of Cloud Condensation Nuclei (CCN) generally produce higher concentrations of cloud droplets, which are also usually assumed to lead to decreased cloud droplet sizes. The result is an increase in cloud albedo, producing a net radiative cooling, opposite to the warming caused by greenhouse gases (Charlson et al. 1992). The change in clouds that is directly induced by an increase of aerosol concentration is an increase of cloud droplet number density, N; but is is usually assumed that cloud droplet size decreases as if the water mass density Liquid Water Content (LWC) were constant. There is actually no reason why this should be the case. Shifting the cloud droplet size distribution to more numerous smaller droplets can change the relative rates of condensational and coalescence growth, leading to different LWC (e.g., Rossow 1978). Moreover, the resulting change in cloud albedo is usually ascribed to more efficient scattering by smaller droplets, when in fact it is the increase in droplet number density (assuming constant LWC) that produces the most important change in cloud albedo: e.g., holding N constant and decreasing the droplet size would actually decrease the scattering cross-section and, thus, the albedo much more than it is increased by the increased scattering efficiency.
We study a diffusive energy-balance climate model governed by a nonlinear parabolic partial differential equation. Three positive steady-state solutions of this equation are found; they correspond to three possible climates of our planet: an interglacial (nearly identical to the present climate), a glacial, and a completely ice-covered earth. We consider also models similar to the main one studied, and determine the number of their steady states. All the models have albedo continuously varying with latitude and temperature, and entirely diffusive horizontal heat transfer. The diffusion is taken to be nonlinear as well as linear. We investigate the stability under small perturbations of the main model's climates. A stability criterion is derived, and its application shows that the 'present climate' and the 'deep freeze' are stable, whereas the model's glacial is unstable. A variational principle is introduced to confirm the results of this stability analysis. For a sufficient decrease in solar radiation (about 2%) the glacial and interglacial solutions disappear, leaving the ice-covered earth as the only possible climate.
The albedo of snow is defined as the ratio of reflected to incident solar energy, and it is an important parameter in the earth's radiation budget analysis and in the study of snowpack's thermal conditions. An approximate model for calculating the incident spectral flux for partially cloudy skies is presented. The input parameters for the calculation are atmospheric precipitable water, turbidity, ozone content, surface pressure, the optical thickness of clouds, and the grain size of snow crystals. The spectral snow reflectance model considers both specular surface reflection and volumetric multiple scattering. The surface reflection is calculated by using a crystal-shape-dependent bidirectional reflectance distribution function; the volumetric multiple scattering is calculated by using a crystal-size-dependent approximate solution in the radiative transfer equation. The model yields spectral and integrated solar flux and snow reflectance as a function of solar elevation and fractional cloud-cover. The illustrative insolation and albedo values were obtained from spectral reflectance and incident flux for representative parameters of Antarctic coastal regions. A simple relationship between grain size and the overcast albedo was obtained. For a set of grain size and shape, the albedo as a function of solar elevation and fractional cloud cover was tabulated.