Regional and global projections of twenty-first century glacier mass changes in response to climate scenarios from global climate models

A large component of present-day sea-level rise is due to the melt of glaciers other than the ice sheets. Recent projections of their contribution to global sea-level rise for the twenty-first century range between 70 and 180 mm, but bear significant uncertainty due to poor glacier inventory and lack of hypsometric data. Here, we aim to update the projections and improve quantification of their uncertainties by using a recently released global inventory containing outlines of almost every glacier in the world. We model volume change for each glacier in response to transient spatially-differentiated temperature and precipitation projections from 14 global climate models with two emission scenarios (RCP4.5 and RCP8.5) prepared for the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. The multi-model mean suggests sea-level rise of 155 ± 41 mm (RCP4.5) and 216 ± 44 mm (RCP8.5) over the period 2006–2100, reducing the current global glacier volume by 29 or 41 %. The largest contributors to projected global volume loss are the glaciers in the Canadian and Russian Arctic, Alaska, and glaciers peripheral to the Antarctic and Greenland ice sheets. Although small contributors to global volume loss, glaciers in Central Europe, low-latitude South America, Caucasus, North Asia, and Western Canada and US are projected to lose more than 80 % of their volume by 2100. However, large uncertainties in the projections remain due to the choice of global climate model and emission scenario. With a series of sensitivity tests we quantify additional uncertainties due to the calibration of our model with sparsely observed glacier mass changes. This gives an upper bound for the uncertainty range of ±84 mm sea-level rise by 2100 for each projection.     

Climate-model induced differences in the 21st century global and regional glacier contributions to sea-level rise

The large uncertainty in future global glacier volume projections partly results from a substantial range in future climate conditions projected by global climate models. This study addresses the effect of global and regional differences in climate input data on the projected twenty-first century glacier contribution to sea-level rise. Glacier volume changes are calculated with a surface mass balance model combined with volume-area scaling, applied to 89 glaciers in different climatic regions. The mass balance model is based on a simplified energy balance approach, with separated contributions by net solar radiation and the combined other fluxes. Future mass balance is calculated from anomalies in air temperature, precipitation and atmospheric transmissivity, taken from eight global climate models forced with the A1B emission scenario. Regional and global sea-level contributions are obtained by scaling the volume changes at the modelled glaciers to all glaciers larger than 0.1 km² outside the Greenland and Antarctic ice sheets. This results in a global value of 0.102 ± 0.028 m (multi-model mean and standard deviation) relative sea-level equivalent for the period 2012–2099, corresponding to 18 ± 5 % of the estimated total volume of glaciers. Glaciers in the Antarctic, Alaska, Central Asia and Greenland together account for 65 ± 4 % of the total multi-model mean projected sea-level rise. The projected sea-level contribution is 35 ± 17 % larger when only anomalies in air temperature are taken into account, demonstrating an important compensating effect by increased precipitation and possibly reduced atmospheric transmissivity. The variability in projected precipitation and atmospheric transmissivity changes is especially large in the Arctic regions, making the sea-level contribution for these regions particularly sensitive to the climate model used. Including additional uncertainties in the modelling procedure and the input data, the total uncertainty estimate for the future projections becomes ±0.063 m.     

Contribution of glacier melt to sea-level rise since AD 1865: a regionally differentiated calculation

 The contribution of glacier melt, including the Greenland ice-sheet, to sea-level change since AD 1865 is estimated on the basis of modelled sensitivity of glacier mass balance to climate change and historical temperature data. Calculations are done in a regionally differentiated manner to overcome the inhomogeneity of the global distribution of glaciers. A distinction is made between changes in summer temperature and in temperature over the rest of the year. Our best estimate of the ice melt in the period 1865–1990 in terms of sea-level change equivalent is 5.7 cm (2.7 cm for glaciers and 3.0 cm for the Greenland ice-sheet). Additional calculations show that simpler methods, like using annual or even global mean temperature anomaly give estimates that differ by up to 55%. Consequently, a regionally differentiating approach is advised for making projections of glacier melt with GCM output. Received: 6 December 1996/Accepted: 30 May 1997     

The 2001 Mesoscale Convective Systems over Iberia and the Balearic Islands

Summary This paper characterizes Mesoscale Convective Systems (MCSs) during 2001 over Iberia and the Balearic Islands and their meteorological settings. Enhanced infrared Meteosat imagery has been used to detect their occurrence over the Western Mediterranean region between June and December 2001 according to satellite-defined criteria based on the MCS physical characteristics. Twelve MCSs have been identified. The results show that the occurrence of 2001 MCSs is limited to the August–October period, with September being the most active period. They tend to develop during the late afternoon or early night, with preferred eastern Iberian coast locations and eastward migrations. A cloud shield area of 50.000 km² is rarely exceeded. When our results are compared with previous studies, it is possible to assert that though 2001 MCS activity was moderate, the convective season was substantially less prolonged than usual, with shorter MCS life cycles and higher average speeds. The average MCS precipitation rate was 3.3 mm·h⁻¹ but a wide range of values varying from scarce precipitation to intense events of 130 mm·24 h⁻¹ (6 September) were collected. The results suggest that, during 2001, MCS rainfall was the principal source of precipitation in the Mediterranean region during the convective season, but its impact varied according to the location. Synoptic analysis based on NCEP/NCAR reanalysis show that several common precursors could be identified over the Western Mediterranean Sea when the 2001 MCSs occurred: a low-level tongue of moist air and precipitable water (PW) exceeding 25 mm through the southern portion of the Western Mediterranean area, low-level zonal warm advection over 2 °C·24 h⁻¹ towards eastern Iberia, a modest 1000–850 hPa equivalent potential temperature (θ_e) difference over 20 °C located close to the eastern Iberian coast, a mid level trough (sometimes a cut-off low) over Northern Africa or Southern Spain and high levels geostrophic vorticity advection exceeding 12·10⁻¹⁰ s⁻² over eastern Iberia and Northern Africa. Finally, the results suggest that synoptic, orographic and a warm-air advection were the most relevant forcing mechanisms during 2001.     

The regional nature of global challenges: a need and strategy for integrated regional modeling

Glaciers of the conterminous United States have been receding for the past century. Since 1900 the recession has varied from a 24 % loss in area (Mt. Rainier, Washington) to a 66 % loss in the Lewis Range of Montana. The rates of retreat are generally similar with a rapid loss in the early decades of the 20th century, slowing in the 1950s–1970s, and a resumption of rapid retreat starting in the 1990s. Decadal estimates of changes in glacier area for a subset of 31 glaciers from 1900 to 2000 are used to test a snow water equivalent model that is subsequently employed to examine the effects of temperature and precipitation variability on annual glacier area changes for these glaciers. Model results indicate that both winter precipitation and winter temperature have been important climatic factors affecting the variability of glacier variability during the 20th Century. Most of the glaciers analyzed appear to be more sensitive to temperature variability than to precipitation variability. However, precipitation variability is important, especially for high elevation glaciers. Additionally, glaciers with areas greater than 1 km² are highly sensitive to variability in temperature.     

Reconstructing sea level from paleo and projected temperatures 200 to 2100 ad

We use a physically plausible four parameter linear response equation to relate 2,000 years of global temperatures and sea level. We estimate likelihood distributions of equation parameters using Monte Carlo inversion, which then allows visualization of past and future sea level scenarios. The model has good predictive power when calibrated on the pre-1990 period and validated against the high rates of sea level rise from the satellite altimetry. Future sea level is projected from intergovernmental panel on climate change (IPCC) temperature scenarios and past sea level from established multi-proxy reconstructions assuming that the established relationship between temperature and sea level holds from 200 to 2100 ad. Over the last 2,000 years minimum sea level (−19 to −26 cm) occurred around 1730 ad, maximum sea level (12–21 cm) around 1150 ad. Sea level 2090–2099 is projected to be 0.9 to 1.3 m for the A1B scenario, with low probability of the rise being within IPCC confidence limits.     

Development of the water budget for three extra-tropicalcyclones with intense rainfall over Europe

Summary  Three cyclones developing between 28 August and 6 September 1995 were studied with respect to the temporal evolution of their water budget components. The cyclones were simulated with the regional model REMO. Water budget values were determined from hourly model output for circle areas with 500 km radius around the pressure minimum. The results show a maximum liquid water path of about 0.12 kg m⁻² and a maximum ice water path of 0.16 kg m⁻². In the vertical cloud structure the medium cloud layer disappears at the end of the life cycle for all three cyclones. The release of precipitation onto the Baltic Sea drainage basin is different for each cyclone. It lies between 13 and 22 · 10¹² kg. This is about 50% of the total precipitation in the whole area for the strongest cyclone and 65% for the others. The P — E (precipitation minus evaporation) is 15 · 10¹² kg for two of the cyclones and 10 · 10¹² kg for the third one. Received August 7, 2000 Revised March 19, 2001     

Rain-aerosol coupling in the tropical atmosphere of Southeast Asia: distribution and scavenging ratios of major ionic species

Both aerosol and rainwater samples were collected and analyzed for ionic species at a coastal site in Southeast Asia over a period of 9 months (January–September 2006) covering different monsoons. In general, the occurrence and distribution of ionic species showed a distinct seasonal variation in response to changes in air mass origins. Real-time physical characterization of aerosol particles during rain events showed changes in particle number distributions which were used to assess particle removal processes associated with precipitation, or scavenging. The mean scavenging coefficients for particles in the range 10–500 nm and 500–10 μm were 7.0 × 10⁻⁵ ± 2.8 × 10⁻⁵ s⁻¹ and 1.9 × 10⁻⁴ ± 1.6 × 10⁻⁵ s⁻¹, respectively. A critical analysis of the scavenging coefficients obtained from this study suggested that the wet removal of aerosol particles was greatly influenced by rain intensity, and was particle size-dependent as well. The scavenging ratios, another parameter used to characterize particle removal processes by precipitation, for NH₄ ⁺, Cl⁻, SO₄ ²⁻, and NO₃ ⁻ were found to be higher than those of Na⁺, K⁺, and Ca²⁺ of oceanic and crustal origins. This enrichment implied that gaseous species NH₃, HCl, and HNO₃ could also be washed out readily. These additional sources of ions in precipitation presumably counter-balanced the dilution effect caused by high total precipitation volume in the marine and tropical area.     

Representing glaciers in a regional climate model

A glacier parameterization scheme has been developed and implemented into the regional climate model REMO. The new scheme interactively simulates the mass balance as well as changes of the areal extent of glaciers on a subgrid scale. The temporal evolution and the general magnitude of the simulated glacier mass balance in the European Alps are in good accordance with observations for the period 1958–1980, but the strong mass loss towards the end of the twentieth century is systematically underestimated. The simulated decrease of glacier area in the Alps between 1958 and 2003 ranges from −17.1 to −23.6%. The results indicate that observed glacier mass balances can be approximately reproduced within a regional climate model based on simplified concepts of glacier-climate interaction. However, realistic results can only be achieved by explicitly accounting for the subgrid variability of atmospheric parameters within a climate model grid box.     

Greenland��s contribution to global sea-level rise by the end of the 21st century

The Greenland ice sheet holds enough water to raise the global sea level with ??7 m. Over the last few decades, observations manifest a substantial increase of the mass loss of this ice sheet. Both enhanced melting and increase of the dynamical discharge, associated with calving at the outlet-glacier fronts, are contributing to the mass imbalance. Using a dynamical and thermodynamical ice-sheet model, and taking into account speed up of outlet glaciers, we estimate Greenland??s contribution to the 21st-century global sea-level rise and the uncertainty of this estimate. Boundary fields of temperature and precipitation extracted from coupled climate-model projections used for the IPCC Fourth Assessment Report, are applied to the ice-sheet model. We implement a simple parameterization for increased flow of outlet glaciers, which decreases the bias of the modeled present-day surface height. It also allows for taking into account the observed recent increase in dynamical discharge, and it can be used for future projections associated with outlet-glacier speed up. Greenland contributes 0?C17?cm to global sea-level rise by the end of the 21st century. This range includes the uncertainties in climate-model projections, the uncertainty associated with scenarios of greenhouse-gas emissions, as well as the uncertainties in future outlet-glacier discharge. In addition, the range takes into account the uncertainty of the ice-sheet model and its boundary fields.     

Mesoscale Convective System over the Yellow Sea – A Numerical Case Study

Summary  A mesoscale convective system (MCS) case that developed over the Yellow Sea (12–13 July 1993) is studied by using a 23-level, 30 km-mesh Penn State/NCAR mesoscale model MM5. This MCS was generated in northern China, south of the Changma front, in a convectively unstable environment, under the influence of a short-wave trough accompanied by a marked cold vortex aloft. The model with all model physics (refereed to as CNTL) captured the major features of this MCS. A mesoscale low-level jet (mLLJ), with a horizontal scale of a few hundred km, developed within the MCS. Available wind data support the realism of this mLLJ. This mLLJ not only transports convectively unstable air directly toward the MCS but is also responsible for a strong low-level convergence in the MCS. At 200 hPa, an anticyclonic northwesterly flow with a relatively high wind speed core on the east of MCS was simulated. This relatively high-speed flow can be regarded as a mesoscale upper level jet (mULJ), acted as an upper outflow over the MCS. Low-level convergence on the left-front of the mLLJ and upper divergence in the right-rear of the mULJ creates a strong upward motion (≅ 40 cm s⁻¹) in the MCS. Heavy precipitation up to 45 mm between 1800–2100 UTC was observed after this MCS landed on the southern Korean Peninsula. The CNTL run captured this heavy rainfall event. A maximum rainfall of 50 mm 3 h⁻¹ was simulated. In another experiment, with surface sensible and moisture fluxes withheld (NOSF), the 3-h simulated rainfall was decreased to 30 mm. Less latent heat released in the NOSF led to a weaker MCS and mLLJ. The concurrent surface fluxes sustained a high low-level moisture field over the Yellow Sea, which helped the development of the MCS and enhanced its precipitation in this case. Received January 8, 1999     

Modelling the response of glaciers to climate warming

 Dynamic ice-flow models for 12 glaciers and ice caps have been forced with various climate change scenarios. The volume of this sample spans three orders of magnitude. Six climate scenarios were considered: from 1990 onwards linear warming rates of 0.01, 0.02 and 0.04 K a^-1, with and without concurrent changes in precipitation. The models, calibrated against the historic record of glacier length where possible, were integrated until 2100. The differences in individual glacier responses are very large. No straightforward relationship between glacier size and fractional change of ice volume emerges for any given climate scenario. The hypsometry of individual glaciers and ice caps plays an important role in their response, thus making it difficult to generalize results. For a warming rate of 0.04 K a^-1, without increase in precipitation, results indicate that few glaciers would survive until 2100. On the other hand, if the warming rate were to be limited to 0.01 K a^-1 with an increase in precipitation of 10% per degree warming, we predict that overall loss would be restricted to 10 to 20% of the 1990 volume. Received: 30 June 1997/Accepted: 21 October 1997     

A Case of Convection Development over the Western Mediterranean Sea: A Study through Numerical Simulations

Summary  A convective case producing heavy precipitation in the western Mediterranean region, characterized by pronounced upper level forcing and main rainfall over the sea, is studied. On the day of the event (September 28^th, 1994), more than 140 mm of precipitation were recorded in coastal lands of eastern Spain, and 180 mm were estimated over the sea with radar data. Synoptically, the case appears to combine warm and moist easterly advection at low levels, typically observed in torrential rainfall events of the region, with a less common strong upper level dynamical forcing. A set of mesoscale numerical simulations using the Hirlam model is performed to investigate the mechanisms responsible for the convection development, and to assess the influence of the orography on the rainfall field. Model output diagnosis indicates that in addition to the lower level forcing, a two-jets interaction is decisive for the triggering and driving of the convection during the event. Moreover, a non-topographic simulation reveals a relatively weak influence of the orography on this event when compared with other similar heavy precipitation cases in eastern Spain. Previous studies have shown an orographic influence of more than 90% on the rainfall whereas in this case about 50% of the precipitation over the area is attributed to the orographic forcing. The study is extended with an analysis of the individual effects of the Atlas and Iberian Peninsula, by means of a factor separation technique. It is shown that the Atlas range induces a redistribution of the precipitation over the Mediterranean, whereas local enhancements can be attributed to the Iberian topography. Received March 2, 1999     

The Trident Pacific model. Part 1: simulating surface ocean currents with a linear model during the 1993–1998 TOPEX/POSEIDON period

 Zonal advection by long equatorial waves has been shown to be an important process in the evolution of sea surface temperature in the central Pacific on ENSO time scales. The present study aims at investigating how well an oceanic model whose dynamics are based on long equatorial waves can simulate the large-scale surface zonal current variability. Thus an ocean linear model which can be run with two or three layers is validated against several sets of observations in the Pacific ocean (TOPEX/POSEIDON sea level, TAO zonal currents, surface current climatology). The surface layer (mixed-layer) has a constant depth. Therefore the layer model is equivalent to considering a shear layer solution and either one or two baroclinic modes. It allows evaluation of the impact of adding a second baroclinic mode on the simulation of surface currents. This evaluation is done for different friction parametrizations: a weak linear Rayleigh friction (24 months⁻¹), a strong linear Rayleigh friction (6 months⁻¹), and a new parametrization using quadratic friction in the momentum equation only. It is shown in all simulations using various Rayleigh friction parametrizations that the addition of a second baroclinic mode always improves the simulation of both the sea level and the surface currents, especially in the central western Pacific. In that region, there is a reduction of the propagating long Rossby waves whose amplitude is much too large when only one baroclinic mode is used. Despite this reduction, the use of a weak friction (24 months⁻¹) always yields results which compare only poorly to observations confirming results from previous studies. The use of strong friction (6 months⁻¹) improves the model simulation, but surface current variability still remains too large. Finally, the use of quadratic friction as proposed in the present study considerably improves the simulation of zonal currents and its comparison to all data sets. This result gives more confidence in the choice of such a simple model to further explore the role of zonal advection by long equatorial waves on ENSO time scales. Received: 28 May 1999 / Accepted: 18 May 2000     

Fine-Scale Observations of Summertime Precipitation in an Intra-Alpine Region

Summary ?Intra-mountain summertime precipitation was studied in the Alps in a 40×20 km² area centered around Innsbruck, Austria, from June through September 1997. An observational network with a mean separation distance of 9 km and forecasts from the ECMWF model were used to examine the role the strong forcing from the lower boundary plays in creating “hot spots” for the formation of thunderstorms and the location of heavy precipitation as well as systematic precipitation patterns for different weather situations, which can be used to downscale forecasts from global scale routine numerical weather prediction models. Received March 16, 1999/Revised August 20, 1999     

Climate change in northern Patagonia: critical decrease in water resources

The current study presents an assessment of the impact of climate change on water yield, one of the main hydrological ecosystem services, in northern Patagonia. The outputs of regional climate models from the CORDEX Project for South America were used to drive the InVEST water yield model. CORDEX regional climate models project for the far future (2071–2100) an increase in temperature higher than 1.5 °C and a precipitation decrease ranging from − 10 to − 30% for the study area. The projected warmer and dryer climate emerges as a robust signal based on model agreement and on consistent physical drivers of these changes. Moreover, both the projected increase in evapotranspiration and the decrease in precipitation contribute to a strong decrease in water yield of around − 20 to − 40% in the headwaters of northern Patagonian watersheds. Comparison of the results in the two basins reveals that the land cover may be considered a buffer of water yield changes and highlights the key role of protected areas in reducing the vulnerability of water resources to climate change.     

Simulated Antarctic precipitation and surface mass balance at the end of the twentieth and twenty-first centuries

The aim of this work is to assess potential future Antarctic surface mass balance changes, the underlying mechanisms, and the impact of these changes on global sea level. To this end, this paper presents simulations of the Antarctic climate for the end of the twentieth and twenty-first centuries. The simulations were carried out with a stretched-grid atmospheric general circulation model, allowing for high horizontal resolution (60 km) over Antarctica. It is found that the simulated present-day surface mass balance is skilful on continental scales. Errors on regional scales are moderate when observed sea surface conditions are used; more significant regional biases appear when sea surface conditions from a coupled model run are prescribed. The simulated Antarctic surface mass balance increases by 32 mm water equivalent per year in the next century, corresponding to a sea level decrease of 1.2 mm year⁻¹ by the end of the twenty-first century. This surface mass balance increase is largely due to precipitation changes, while changes in snow melt and turbulent latent surface fluxes are weak. The temperature increase leads to an increased moisture transport towards the interior of the continent because of the higher moisture holding capacity of warmer air, but changes in atmospheric dynamics, in particular off the Antarctic coast, regionally modulate this signal.     

Net CO2 exchange of a subarctic mountain birch ecosystem

Summary  Net ecosystem CO₂ exchange was measured over a mountain birch forest in northern Finland throughout the growing season. The maximal net CO₂ uptake rate of about − 0.5 mg(CO₂) m⁻² s⁻¹ was observed at the end of July. The highest nocturnal respiration rates in early August were 0.2 mg(CO₂) m⁻² s⁻¹. The daily CO₂ balances during the time of maximal photosynthesis were about −15 g(CO₂) m⁻² d⁻¹. The mountain birch forest acted as a net sink of CO₂ from 30 June to 28 August. During that period the net CO₂ balance was −448 g(CO₂)m⁻². The interannual representativeness of the observed balances was studied using a simplified daily balance model, with daily mean global radiation and air temperature as the input parameters. The year-to-year variation in the phenological development was parameterised as a function of the cumulative effective temperature sum. The daily balance model was used for estimating the variability in the seasonal CO₂ balances due to the timing of spring and meteorological factors. The sink term of CO₂ in 1996 was lower than the 15-year mean, mainly due to the relatively late emergence of the leaves. Received October 11, 1999 Revised April 25, 2000     

A precipitation-dominated,mid-latitude glacier system: Mount Shasta,California

Temperature is often seen as the dominant control on inter-decadal glacier volume changes. However, despite regional warming over the past half-century, the glaciers of Mount Shasta have continued to expand following a contraction during a prolonged drought in the early twentieth century, indicating a greater sensitivity to precipitation than temperature. We use the 110 year record of fluctuations in Mount Shasta’s glaciers and climate to calibrate numerical glacier models of the two largest glaciers. The reconstructed balance and volume histories show a much greater correlation to precipitation than temperature and significant correlation to oscillatory modes of Pacific Ocean climate. An approximately 20% increase in precipitation is needed for every 1°C increase in temperature to maintain stability. Under continued historical trends, oscillations in climate modes and random variability will dominate inter-decadal variability in ice volume. Under the strong warming trend predicted by a regional climate model, the temperature trend will be the dominant forcing resulting in near total loss of Mount Shasta’s glaciers by the end of the twenty-first century.Electronic Supplementary Material Supplementary material is available to authorised users in the online version of this article at .     

Clear-sky aerosol radiative forcing effects based on multi-site AERONET observations over Europe

Summary One of the great unknowns in climate research is the contribution of aerosols to climate forcing and climate perturbation. In this study, retrievals from AERONET are used to estimate the direct clear-sky aerosol top-of-atmosphere and surface radiative forcing effects for 12 multi-site observing stations in Europe. The radiative transfer code sdisort in the libRadtran environment is applied to accomplish these estimations. Most of the calculations in this study rely on observations which have been made for the years 1999, 2000, and 2001. Some stations do have observations dating back to the year of 1995. The calculations rely on a pre-compiled aerosol optical properties database for Europe. Aerosol radiative forcing effects are calculated with monthly mean aerosol optical properties retrievals and calculations are presented for three different surface albedo scenarios. Two of the surface albedo scenarios are generic by nature bare soil and green vegetation and the third relies on the ISCCP (International Satellite Cloud Climatology Project) data product. The ISCCP database has also been used to obtain clear-sky weighting fractions over AERONET stations. The AERONET stations cover the area 0° to 30° E and 42° to 52° N. AERONET retrievals are column integrated and this study does not make any seperation between the contribution of natural and anthropogenic components. For the 12 AERONET stations, median clear-sky top-of-atmosphere aerosol radiative forcing effect values for different surface albedo scenarios are calculated to be in the range of −4 to −2 W/m². High median radiative forcing effect values of about −6 W/m² were found to occur mainly in the summer months while lower values of about −1 W/m² occur in the winter months. The aerosol surface forcing also increases in summer months and can reach values of −8 W/m². Individual stations often have much higher values by a factor of 2. The median top-of-atmosphere aerosol radiative forcing effect efficiency is estimated to be about −25 W/m² and their respective surface efficiency is around −35 W/m². The fractional absorption coefficient is estimated to be 1.7, but deviates significantly from station to station. In addition, it is found that the well known peak of the aerosol radiative forcing effect at a solar zenith angle of about 75° is in fact the average of the peaks occurring at shorter and longer wavelengths. According to estimations for Central Europe, based on mean aerosol optical properties retrievals from 12 stations, the critical threshold of the aerosol single scattering albedo, between cooling and heating in the presence of an aerosol layer, is close between 0.6 and 0.76.