scholarly journals Microwave Emissivity and Accumulation Rate of Polar Firn

1977 ◽  
Vol 18 (79) ◽  
pp. 195-215 ◽  
Author(s):  
H. Jay Zwally
Keyword(s):  
Radiative Transfer ◽  
Rayleigh Scattering ◽  
Accumulation Rate ◽  
Snow Accumulation ◽  
Empirical Parameter ◽  
Microwave Brightness Temperature ◽  
Scattering Coefficients ◽  
Microwave Emissivity ◽  
Snow Crystal ◽  
The Mean

Abstract Radiative transfer theory is formulated to permit a meaningful definition of emissivity for bulk emitting media such as snow. The emissivity in the Rayleigh-Jeans approximation is then the microwave brightness temperature T B divided by an effective physical temperature 〈T〉. The 〈T〉 is an average of the physical temperature, T(z), weighted by a radiative transfer function ƒ(z). Similarly, where e(z) is the local emittance. An approximate ƒ(z) is used to determine analytically the effects of various absorption coefficients, of scattering coefficients that vary with depth, and of the seasonal variation of T(z). It is shown that a mean emissivity, which is equal to the mean annual T B divided by the mean annual surface temperature T m, is a useful quantity for comparing theory and observations. Snow-crystal size measurements, r(z), at seven locations in Greenland and Antarctica are used to determine the Mie/Rayleigh scattering coefficient γs (z and to calculate the mean emissivities. The observed mean emissivities are determined by a which is the average of 12 monthly Nimbus-5 (1.55 cm) microwave observations, and the Tm measured at the same locations. The calculated emissivities are about one-half of the observed values. The assumption that each snow crystal is an independent and equally effective scatterer, and the use of an approximation to ƒ(z), tend to over-estimate the effect of scattering. Therefore, a parameter multiplying γs (z) is used. The emissivities calculated with a single value of this empirical parameter for all seven locations agree well with the observed emissivities, showing that the microwave emissivity variations of dry polar urn can be characterised as a function of the crystal sizes. One optical depth corresponds to a typical fini depth of 5 m, but significant radiation emanates from up to 30 m. Since r(z) depends on the snow accumulation rate A and T m. the sensitivity of the emissivity to changes in T m or A are estimated using this semi-empirical theory. The results show that a one degree change or uncertainty in Tm is approximately equivalent to a 10% change in A, and that such a change will affect the emissivity by 0.003 to 0.014 or the T B by about 0.6 K to 3 K, depending on the location.

scholarly journals Microwave Emissivity and Accumulation Rate of Polar Firn

1977 ◽  
Vol 18 (79) ◽  
pp. 195-215 ◽  
Author(s):  
H. Jay Zwally
Keyword(s):  
Radiative Transfer ◽  
Rayleigh Scattering ◽  
Accumulation Rate ◽  
Snow Accumulation ◽  
Empirical Parameter ◽  
Microwave Brightness Temperature ◽  
Scattering Coefficients ◽  
Microwave Emissivity ◽  
Snow Crystal ◽  
The Mean

AbstractRadiative transfer theory is formulated to permit a meaningful definition of emissivity for bulk emitting media such as snow. The emissivity in the Rayleigh-Jeans approximation is then the microwave brightness temperature TB divided by an effective physical temperature 〈T〉. The 〈T〉 is an average of the physical temperature, T(z), weighted by a radiative transfer function ƒ(z). Similarly, where e(z) is the local emittance. An approximate ƒ(z) is used to determine analytically the effects of various absorption coefficients, of scattering coefficients that vary with depth, and of the seasonal variation of T(z). It is shown that a mean emissivity, which is equal to the mean annual TB divided by the mean annual surface temperature Tm, is a useful quantity for comparing theory and observations. Snow-crystal size measurements, r(z), at seven locations in Greenland and Antarctica are used to determine the Mie/Rayleigh scattering coefficient γs(z) and to calculate the mean emissivities. The observed mean emissivities are determined by a which is the average of 12 monthly Nimbus-5 (1.55 cm) microwave observations, and the Tm measured at the same locations. The calculated emissivities are about one-half of the observed values. The assumption that each snow crystal is an independent and equally effective scatterer, and the use of an approximation to ƒ(z), tend to over-estimate the effect of scattering. Therefore, a parameter multiplying γs(z) is used. The emissivities calculated with a single value of this empirical parameter for all seven locations agree well with the observed emissivities, showing that the microwave emissivity variations of dry polar urn can be characterised as a function of the crystal sizes. One optical depth corresponds to a typical fini depth of 5 m, but significant radiation emanates from up to 30 m. Since r(z) depends on the snow accumulation rate A and Tm. the sensitivity of the emissivity to changes in Tm or A are estimated using this semi-empirical theory. The results show that a one degree change or uncertainty in Tm is approximately equivalent to a 10% change in A, and that such a change will affect the emissivity by 0.003 to 0.014 or the TB by about 0.6 K to 3 K, depending on the location.

Radiative transfer: exact Rayleigh scattering series and a formula for daylight

2007 ◽  
Vol 463 (2086) ◽  
pp. 2729-2751 ◽  
Author(s):  
J.H Hannay
Keyword(s):  
Radiative Transfer ◽  
Rayleigh Scattering ◽  
Numerical Algorithms ◽  
Mean Free Path ◽  
Single Scattering ◽  
Scattering Approximation ◽  
The Status ◽  
The Mean ◽  
Error Order ◽  
Partial Polarization

Daylight, or sky light, is sunlight Rayleigh scattered by the atmosphere onto the ground. This random scattering propagation through clear air is governed by ‘radiative transfer’. Beyond the single-scattering approximation, the famous virtuoso analysis of Chandrasekhar formulated the problem and offered exact, but rather involved, and ultimately numerical, algorithms for its solution. However, there is no real difficulty in writing down directly the exact Rayleigh scattering series in integrals. Its practical utility is limited to fairly small thicknesses T of atmosphere (compared with the mean free path), but the Earth has just such. Here even the next order beyond single scattering (error order T 2 ) supplies a formula for the brightness and partial polarization of daylight across the sky, which captures the essential topology of the polarization pattern, and also remains uniformly valid in the small thickness limit, for all elevations of the Sun and viewing angles. The status of the mathematical polarization direction pattern invented by Berry, Dennis and Lee as the simplest fit to the required topology is clarified.

scholarly journals Snow accumulation rate on Qomolangma (Mount Everest), Himalaya: synchroneity with sites across the Tibetan Plateau on 50–100 year timescales

2008 ◽  
Vol 54 (185) ◽  
pp. 343-352 ◽  
Author(s):  
Susan Kaspari ◽  
Roger LeB. Hooke ◽  
Paul Andrew Mayewski ◽  
Shichang Kang ◽  
Shugui Hou ◽  
...  
Keyword(s):  
Tibetan Plateau ◽  
Accumulation Rate ◽  
Ice Core ◽  
Snow Accumulation ◽  
The Tibetan Plateau ◽  
Mount Everest ◽  
Mountain Meteorology ◽  
Annual Layer ◽  
Decadal Scale ◽  
The Mean

AbstractAnnual-layer thickness data, spanning AD 1534–2001, from an ice core from East Rongbuk Col on Qomolangma (Mount Everest, Himalaya) yield an age–depth profile that deviates systematically from a constant accumulation-rate analytical model. The profile clearly shows that the mean accumulation rate has changed every 50–100 years. A numerical model was developed to determine the magnitude of these multi-decadal-scale rates. The model was used to obtain a time series of annual accumulation. The mean annual accumulation rate decreased from ∼0.8 m ice equivalent in the 1500s to ∼0.3 m in the mid-1800s. From ∼1880 to ∼1970 the rate increased. However, it has decreased since ∼1970. Comparison with six other records from the Himalaya and the Tibetan Plateau shows that the changes in accumulation in East Rongbuk Col are broadly consistent with a regional pattern over much of the Plateau. This suggests that there may be an overarching mechanism controlling precipitation and mass balance over this area. However, a record from Dasuopu, only 125 km northwest of Qomolangma and 700 m higher than East Rongbuk Col, shows a maximum in accumulation during the 1800s, a time during which the East Rongbuk Col and Tibetan Plateau ice-core and tree-ring records show a minimum. This asynchroneity may be due to altitudinal or seasonal differences in monsoon versus westerly moisture sources or complex mountain meteorology.

scholarly journals Spatial and temporal patterns in snow accumulation, western Dronning Maud Land, Antarctica

1994 ◽  
Vol 40 (135) ◽  
pp. 399-409 ◽  
Author(s):  
Elisabeth Isaksson ◽  
Wibjörn Karlén
Keyword(s):  
Temporal Variability ◽  
Accumulation Rate ◽  
Snow Accumulation ◽  
Temperature Record ◽  
Spatial And Temporal Patterns ◽  
Ice Shelf ◽  
Grounding Line ◽  
Antarctic Expedition ◽  
Dronning Maud Land ◽  
The Mean

AbstractDuring the Swedish Antarctic Expedition to Dronning Maud Land, Antarctica, 1988–89 the net accumulation was estimated for an area from the coast to about 400 km inland. Stake measurements were used to obtain the spatial variability and firn cores were used for the temporal variability. The mean annual accumulation for the period 1976–88 is about 0.4mw.e. for Riiser-Larsenisen and about 0.3mw.e. for the area above the grounding line. The accumulation rate at higher altitudes, > 2500 m a.s.1., is about 0.1 m w.e. for 1955–88. One record from the ice shelf covers the period 1957–88, and suggests an increase in accumulation of about 12%. Between 1976 and 1988, the accumulation has decreased by about 50%, most likely due to lower temperatures as suggested by the temperature record from Halley.

scholarly journals Snow accumulation rates in northern Victoria Land, Antarctica, by firn-core analysis

2000 ◽  
Vol 46 (155) ◽  
pp. 541-552 ◽  
Author(s):  
Barbara Stenni ◽  
Francesca Serra ◽  
Massimo Frezzotti ◽  
Valter Maggi ◽  
Rita Traversi ◽  
...  
Keyword(s):  
Accumulation Rate ◽  
Ice Cores ◽  
Snow Accumulation ◽  
Katabatic Wind ◽  
Climatic Data ◽  
Accumulation Rates ◽  
Surface Mass ◽  
Physical Study ◽  
Victoria Land ◽  
The Mean

AbstractA multiparametric (chemical, isotopic and physical) study on three shallow firn cores sampled in northern Victoria Land was carried out to obtain glaciological information and climatic data in this Antarctic region. Sampling areas were accurately prospected to identify sites, located at different altitudes and distances from the sea, where the snow accumulation was not influenced by katabatic wind redistribution or summer melting. Stratigraphic, isotopic (δl8O) and chemical (H2O2, MSA and nssSO42−) profiles were mutually examined for dating purposes and to determine the mean snow-accumulation rates at three different stations. Annual accumulation rates of 85–420 kg m−2 a−1 were determined in the period 1971–92. An inverse pattern between accumulation rate and altitude was shown by the progression of the mean annual rates of 160, 203 and 260 kg m−2 a−1, respectively, in the highest, medium and lowest stations. The mean accumulation value of all northern Victoria Land data available, 170 kg m−2 a−1, represents a decrease of up to 35% with respect to the estimated value most widely used until now. Our accumulation value is very close to that required for a zero net surface mass balance according to ice discharge. A linear relationship with a gradient of 0.81‰ °C−1 has been found between mean δ18O values and mean annual surface temperature for different ice cores drilled in northern Victoria Land.

scholarly journals Radiative Transfer Modeling of Microwave Emission and Dependence on Firn Properties

1982 ◽  
Vol 3 ◽  
pp. 54-58 ◽  
Author(s):  
J. C. Comiso ◽  
H. J. Zwally ◽  
J. L. Saba
Keyword(s):  
Radiative Transfer ◽  
Rayleigh Scattering ◽  
Index Of Refraction ◽  
Microwave Emission ◽  
Scattering Coefficients ◽  
Brightness Temperatures ◽  
Significant Temperature ◽  
Radiative Transfer Modeling ◽  
Seasonal Dependence ◽  
Good Agreement

The microwave emission from a model polar firn was calculated using a numerical solution of the radiative transfer equation that included angledependent Rayleigh scattering. The depth-dependent parameters in the equation were physical temperature and the coefficients of scattering and absorption. The coefficients were based on Rayleigh scattering from the snow grains. The bulk emissivity and the seasonal dependence of brightness temperature were calculated for seven locations at which grain sizes were measured as a function of depth. When the absorption and scattering coefficients are adjusted, the modeled emissivities agree with observed emissivities at these locations. The modeled seasonal dependence of brightness temperatures also compares well with values obtained at 1.55 cm wavelength by the Nimbus-5 satellite. Good agreement with data did not occur when the imaginary part of the index of refraction (and, hence, the absorption coefficient) had a significant temperature dependence between 210 and 250 K.

scholarly journals Firn accumulation records for the past 1000 years on the basis of dielectric profiling of six cores from Dronning Maud Land, Antarctica

2004 ◽  
Vol 50 (169) ◽  
pp. 279-291 ◽  
Author(s):  
Coen M. Hofstede ◽  
S.W van de Wal Roderik ◽  
Karsten A. Kaspers ◽  
Michiel R. van den Broeke ◽  
Lars Karlöf ◽  
...  
Keyword(s):  
20Th Century ◽  
Accumulation Rate ◽  
Ice Cores ◽  
Snow Accumulation ◽  
The Past ◽  
Medium Length ◽  
Dronning Maud Land ◽  
The Mean ◽  
Firn Core ◽  
Past 1000 Years

AbstractThis paper presents an overview of firn accumulation in Dronning Maud Land (DML), Antarctica, over the past 1000 years. It is based on a chronology established with dated volcanogenic horizons detected by dielectric profiling of six medium-length firn cores. In 1998 the British Antarctic Survey retrieved a medium-length firn core from western DML. During the Nordic EPICA (European Project for Ice Coring in Antarctica) traverse of 2000/01, a 160 m long firn core was drilled in eastern DML. Together with previously published data from four other medium-length ice cores from the area, these cores yield 50 possible volcanogenic horizons. All six firn cores cover a mutual time record until the 29th eruption. This overlapping period represents a period of approximately 1000 years, with mean values ranging between 43 and 71 mm w.e. The cores revealed no significant trend in snow accumulation. Running averages over 50 years, averaged over the six cores, indicate temporal variations of5%. All cores display evidence of a minimum in the mean annual firn accumulation rate around AD 1500 and maxima around AD 1400 and 1800. The mean increase over the early 20th century was the strongest increase, but the absolute accumulation rate was not much higher than around AD 1400. In eastern DML a 13% increase is observed for the second half of the 20th century.

scholarly journals Spatial and temporal patterns in snow accumulation, western Dronning Maud Land, Antarctica

1994 ◽  
Vol 40 (135) ◽  
pp. 399-409 ◽  
Author(s):  
Elisabeth Isaksson ◽  
Wibjörn Karlén
Keyword(s):  
Temporal Variability ◽  
Accumulation Rate ◽  
Snow Accumulation ◽  
Temperature Record ◽  
Spatial And Temporal Patterns ◽  
Ice Shelf ◽  
Grounding Line ◽  
Antarctic Expedition ◽  
Dronning Maud Land ◽  
The Mean

AbstractDuring the Swedish Antarctic Expedition to Dronning Maud Land, Antarctica, 1988–89 the net accumulation was estimated for an area from the coast to about 400 km inland. Stake measurements were used to obtain the spatial variability and firn cores were used for the temporal variability. The mean annual accumulation for the period 1976–88 is about 0.4mw.e. for Riiser-Larsenisen and about 0.3mw.e. for the area above the grounding line. The accumulation rate at higher altitudes, > 2500 m a.s.1., is about 0.1 m w.e. for 1955–88. One record from the ice shelf covers the period 1957–88, and suggests an increase in accumulation of about 12%. Between 1976 and 1988, the accumulation has decreased by about 50%, most likely due to lower temperatures as suggested by the temperature record from Halley.

scholarly journals Radiative Transfer Modeling of Microwave Emission and Dependence on Firn Properties

1982 ◽  
Vol 3 ◽  
pp. 54-58 ◽  
Author(s):  
J. C. Comiso ◽  
H. J. Zwally ◽  
J. L. Saba
Keyword(s):  
Radiative Transfer ◽  
Rayleigh Scattering ◽  
Index Of Refraction ◽  
Microwave Emission ◽  
Scattering Coefficients ◽  
Brightness Temperatures ◽  
Significant Temperature ◽  
Radiative Transfer Modeling ◽  
Seasonal Dependence ◽  
Good Agreement

The microwave emission from a model polar firn was calculated using a numerical solution of the radiative transfer equation that included angledependent Rayleigh scattering. The depth-dependent parameters in the equation were physical temperature and the coefficients of scattering and absorption. The coefficients were based on Rayleigh scattering from the snow grains. The bulk emissivity and the seasonal dependence of brightness temperature were calculated for seven locations at which grain sizes were measured as a function of depth. When the absorption and scattering coefficients are adjusted, the modeled emissivities agree with observed emissivities at these locations. The modeled seasonal dependence of brightness temperatures also compares well with values obtained at 1.55 cm wavelength by the Nimbus-5 satellite. Good agreement with data did not occur when the imaginary part of the index of refraction (and, hence, the absorption coefficient) had a significant temperature dependence between 210 and 250 K.

Radiative Transfer in Homogeneous Nongray Gases With Nonisotropic Particle Scattering

1974 ◽  
Vol 96 (3) ◽  
pp. 385-390 ◽  
Author(s):  
G. A. Domoto ◽  
W. C. Wang
Keyword(s):  
Radiative Transfer ◽  
Rayleigh Scattering ◽  
Narrow Band ◽  
Perturbation Technique ◽  
Wide Band ◽  
Particle Scattering ◽  
Scattering Coefficients ◽  
Earth’S Atmosphere ◽  
Plane Parallel ◽  
Homogeneous Plane

A perturbation technique is presented to treat the problem of radiative transfer in homogeneous, plane parallel, nongray gases with nonisotropic particle scattering. The technique allows use of nongray narrow-band or wide-band models as well as Mie and Rayleigh scattering coefficients and asymmetry factors. Results are obtained in the form of monochromatic transmittance, reflectance, and absorptance of water clouds typical of those in the earth’s atmosphere.

Sign in / Sign up

Export Citation Format

Share Document