Abstract

A new retrieval algorithm for estimation of snow grain size and impurity concentration from spectral radiation data is developed for remote sensing applications. A radiative transfer (RT) model for the coupled atmosphere-snow system is used as a forward model. This model simulates spectral radiant quantities for visible and near-infrared channels. The forward RT calculation is, however, the most time-consuming part of the forward-inverse modeling. Therefore, we replaced it with a neural network (NN) function for fast computation of radiances and Jacobians. The retrieval scheme is based on an optimal estimation method with a priori constraints. The NN function was also employed to obtain an accurate first guess in the retrieval scheme. Validation with simulation data shows that a combination of NN techniques and optimal estimation method can provide more accurate retrievals than by using only NN techniques. In addition, validation with in-situ measurements conducted by using ground-based spectral radiometer system shows that comparison between retrieved snow parameters with in-situ measurements is acceptable with satisfactory accuracy. The algorithm provides simultaneous, accurate and fast retrieval of the snow properties. The algorithm presented here is useful for airborne/satellite remote sensing.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  44. K. Kuchiki, T. Aoki, M. Niwano, S. Matoba, Y. Kodama, and K. Adachi, “Elemental carbon, organic carbon, and dust concentrations in snow measured with thermal optical and gravimetric methods: variations during the 2007–2013 winters at Sapporo, Japan,” J. Geophys. Res. 120, 868–882 (2015).
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    [Crossref]
  49. T. Tanikawa, T. Aoki, M. Hori, A. Hachikubo, and M. Aniya, “Snow bidirectional reflectance model using non-spherical snow particles and its validation with field measurements,” EARSeL eProceedings 5, 137–145 (2006).
  50. T. Tanikawa, M. Hori, T. Aoki, A. Hachikubo, K. Kuchiki, M. Niwano, S. Matoba, S. Yamaguchi, and K. Stamnes, “In situ measurements of polarization properties of snow surface under the Brewster geometry in Hokkaido, Japan and northwest Greenland ice sheet,” J. Geophys. Res. 119, 13946–13964 (2014).
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2015 (1)

K. Kuchiki, T. Aoki, M. Niwano, S. Matoba, Y. Kodama, and K. Adachi, “Elemental carbon, organic carbon, and dust concentrations in snow measured with thermal optical and gravimetric methods: variations during the 2007–2013 winters at Sapporo, Japan,” J. Geophys. Res. 120, 868–882 (2015).

2014 (3)

T. Tanikawa, M. Hori, T. Aoki, A. Hachikubo, K. Kuchiki, M. Niwano, S. Matoba, S. Yamaguchi, and K. Stamnes, “In situ measurements of polarization properties of snow surface under the Brewster geometry in Hokkaido, Japan and northwest Greenland ice sheet,” J. Geophys. Res. 119, 13946–13964 (2014).

N. Chen, W. Li, T. Tanikawa, M. Hori, T. Aoki, and K. Stamnes, “Cloud mask over snow-/ice-covered areas for the GCOM-C1/SGLI cryosphere mission: Validations over Greenland,” J. Geophys. Res. 119, 12287–12300 (2014).

L. Fan, W. Li, A. Dahlback, J. J. Stamnes, S. Stamnes, and K. Stamnes, “New neural-network-based method to infer total ozone column amounts and cloud effects from multi-channel, moderate bandwidth filter instruments,” Opt. Express 22, 19595–19609 (2014).
[Crossref] [PubMed]

2013 (2)

A. Mary, M. Dumont, J. P. Dedieu, Y. Durand, P. Sirguey, H. Milhem, O. Mestre, H. S. Negi, A. A. Kokhanovsky, M. Lafaysse, and S. Morin, “Intercomparison of retrieval algorithms for the specific surface area of snow from near-infrared satellite data in mountainous terrain, and comparison with the output of a semi-distributed snow-pack model,” The Cryosphere 7, 741–761 (2013).
[Crossref]

H. Wiebe, G. Heygster, E. Zege, T. Aoki, and M. Hori, “Snow grain size retrieval SGSP from optical satellite data: Validation with ground measurements and detection of snow fall events,” Remote Sens. Environ. 128, 11–20 (2013).
[Crossref]

2011 (3)

A. A. Kokhanovsky, V. V. Rozanov, T. Aoki, D. Odermatt, C. Brockmann, O. Krüger, M. Bouvet, M. Drusch, and M. Hori, “Sizing snow grains using backscattered solar light,” Int. J. Remote Sens. 22, 6975–7008 (2011).
[Crossref]

K. Stamnes, B. Hamre, J. J. Stamnes, G. Ryzhikov, M. Biryulina, R. Mahoney, B. Hauss, and A. Sei, “Modeling of radiation transport in coupled atmosphere-snow-ice-ocean systems,” J. Quant. Spectrosc. Radiat. Transfer 112, 714–726 (2011).
[Crossref]

T. Aoki, K. Kuchiki, M. Niwano, Y. Kodama, M. Hosaka, and T. Tanaka, “Physically based snow albedo model for calculating broadband albedos and the solar heating profile in snowpack for general circulation models,” J. Geophys. Res. 116, D11114 (2011).
[Crossref]

2010 (1)

K. Imaoka, M. Kachi, H. Fujii, H. Murakami, M. Hori, A. Ono, T. Igarashi, K. Nakagawa, T. Oki, Y. Honda, and H. Shimoda, “Global Change Observation Mission (GCOM) for monitoring carbon, water cycles, and climate change,” Proc. IEEE 98(5), 717–734 (2010).
[Crossref]

2009 (2)

A. Lyapustin, M. Tedesco, Y. Wang, T. Aoki, M. Hori, and A. A. Kokhanovsky, “Retrieval of snow grain size over Greenland from MODIS,” Remote Sens. Environ. 113, 976–987 (2009).
[Crossref]

K. Kuchiki, T. Aoki, T. Tanikawa, and Y. Kodama, “Retrieval of snow physical parameters using a ground-based spectral radiometer,” Appl. Opt. 48, 5567–5582 (2009).
[Crossref] [PubMed]

2008 (3)

W. Li, K. Stamnes, R. Spurr, and J. J. Stamnes, “Simultaneous retrieval of aerosol and ocean properties by optimal estimation: SeaWiFS case studies for the Santa Barbara Channel,” Int. J. Remote Sens. 29, 5689–5698 (2008).
[Crossref]

S. G. Warren and R. E. Brandt, “Optical constants of ice from the ultraviolet to the microwave: a revised compilation,” J. Geophys. Res. 113, D14220 (2008).
[Crossref]

Z. Jin, T. P. Charlock, P. Yang, Y. Xie, and W. Miller, “Snow optical properties for different particle shapes with application to snow grain size retrieval and MODIS/CERES radiance comparison over Antarctica,” Remote Sens. Environ. 112, 3563–3581 (2008).
[Crossref]

2007 (7)

K. Stamnes, W. Li, H. Eide, T. Aoki, M. Hori, and R. Storvold, “ADEOS-II/GLI snow/ice products: Part I -Scientific basis,” Remote Sens. Environ. 111, 258–273 (2007).
[Crossref]

M. Hori, T. Aoki, K. Stamnes, and W. Li, “ADEOS-II/GLI snow/ice products: Part III - Retrieved results,” Remote Sens. Environ. 111, 291–336 (2007).
[Crossref]

M. Tedesco and A. A. Kokhanovsky, “The semi-analytical snow retrieval algorithm and its application to MODIS data,” Remote Sens. Environ. 111, 228–241 (2007).
[Crossref]

T. Scambos, T. Haran, M. Fahnestock, T. H. Painter, and J. Bohlander, “MODIS-based mosaic of Antarctica (MOA) data sets: Continent-wide surface morphology and snow grain size,” Remote Sens. Environ. 111, 242–257 (2007).
[Crossref]

L. Meng, Y. He, J. Chen, and Y. Wu, “Neural network retrieval of ocean surface parameters from SSM/I data,” Mon. Weather Rev. 135, 586–597 (2007).
[Crossref]

R. Spurr, K. Stamnes, H. Eide, W. Li, K. Zhang, and J. J. Stamnes, “Simultaneous retrieval of aerosols and ocean properties: a classic inverse modeling approach. I. Analytic Jacobians from the linearized CAO-DISORT model,” J. Quantum Spectrosc. Radiat. Transfer 104, 428–449 (2007).
[Crossref]

T. Aoki, M. Hori, H. Motoyohi, T. Tanikawa, A. Hachikubo, K. Sugiura, T. J. Yasunari, R. Storvold, H. Eide, K. Stamnes, W. Li, J. Nieke, Y. Nakajima, and F. Takahashi, “ADEOS-II/GLI snow/ice products: Part II - Validation results using GLI and MODIS data,” Remote Sens. Environ. 111, 274–290 (2007).
[Crossref]

2006 (4)

M. Matzl and M. Schneebeli, “Measuring specific surface area of snow by near-infrared photography,” J. Glaciol. 52, 558–564 (2006).
[Crossref]

T. Tanikawa, T. Aoki, M. Hori, A. Hachikubo, and M. Aniya, “Snow bidirectional reflectance model using non-spherical snow particles and its validation with field measurements,” EARSeL eProceedings 5, 137–145 (2006).

T. Tanikawa, T. Aoki, M. Hori, A. Hachikubo, O. Abe, and M. Aniya, “Monte Carlo simulations of spectral albedo for artificial snowpacks composed of spherical and nonspherical particles,” Appl. Opt. 45, 5310–5319 (2006).
[Crossref] [PubMed]

M. O. Andreae and A. Gelencsér, “Black carbon or brown carbon? The nature of light-absorbing carbonaceous aerosols,” Atmos. Chem. Phys. 6, 3131–3148 (2006).
[Crossref]

2005 (1)

A. A. Kokhanovsky, T. Aoki, A. Hachikubo, M. Hori, and E. P. Zege, “Reflective properties of natural snow: approximate asymptotic theory versus in situ measurements,” IEEE Trans. Geosci. Remote Sens. 43, 1529–1535 (2005).
[Crossref]

2004 (2)

M. Schneebeli and S. A. Sokratov, “Tomography of temperature gradient metamorphism of snow and associated changes in heat conductivity,” Hydrol. Process. 18, 3655–3665 (2004).
[Crossref]

J. Hansen and L. Nazarenko, “Soot climate forcing via snow and ice albedos,” Proc. Natl. Acad. Sci. USA 101, 423–428 (2004).
[Crossref]

2003 (2)

T. Aoki, A. Hachikubo, and M. Hori, “Effects of snow physical parameters on shortwave broadband albedos,” J. Geophys. Res. 108, 4616 (2003).
[Crossref]

J. E. Kay, A. R. Gillespie, G. B. Hansen, and E. C. Pettit, “Spatial relationship between snow contaminant content, grain size, and surface temperature from multispectral images of Mt. Rainier, Washington (USA),” Remote Sens. Environ. 86, 216–231 (2003).
[Crossref]

2002 (1)

T. Tanikawa, T. Aoki, and F. Nishio, “Remote sensing of snow grain size and snow impurities from airborne multispectral scanner data using a snow bidirectional reflectance distribution function model,” Ann. Glaciol. 34, 74–80 (2002).
[Crossref]

2001 (2)

W. Li, K. Stamnes, and B. Chen, “Snow grain size retrieved from near-infrared radiances at multiple wavelengths,” Geophys. Res. Lett. 28, 1699–1702 (2001).
[Crossref]

J. C. Chow, J. G. Watson, D. Crow, D. H. Lowenthal, and T. Merrifield, “Comparison of IMPROVE and NIOSH carbone measurements,” Aerosol Sci. Technol. 34, 23–34 (2001).
[Crossref]

2000 (2)

Te. Aoki, Ta. Aoki, M. Fukabori, A. Hachikubo, Y. Tachibana, and F. Nishio, “Effects of snow physical parameters on spectral albedo and bi-directional reflectance of snow surface,” J. Geophys. Res. 105, 10219–10236 (2000).
[Crossref]

A. W. Nolin and S. Liang, “Progress in bidirectional reflectance modeling and applications for surface particulate media: snow and soils,” Remote Sens. Rev. 18, 307–342 (2000).
[Crossref]

1999 (1)

T. C. Grenfell and S. G. Warren, “Relationship of a nonspherical ice particle by a collection of independent spheres for scattering and absorption of radiation,” J. Geophys. Res. 104, 31697–31709 (1999).
[Crossref]

1998 (2)

M. Hess, P. Koepke, and I. Schult, “Optical properties of aerosols and clouds: the software package OPAC,” Bull. Am. Meteorol. Soc. 79, 831–844 (1998).
[Crossref]

A. Abdelgadir, “Forward and inverse modeling of canopy directional reflectance using a neural network,” Int. J. Remote Sens. 19, 453–471 (1998).
[Crossref]

1997 (2)

P. M. Atkinson and A. R. L. Tatnall, “Neural networks in remote sensing - introduction,” Int. J. Remote Sens. 18, 699–709 (1997).
[Crossref]

M. Fily, B. Bourdelles, J. P. Dedieu, and C. Sergent, “Comparison of in situ and Landsat Thematic mapper derived snow grain characteristics in the Alps,” Remote Sens. Environ. 59, 452–460 (1997).
[Crossref]

1993 (1)

J. C. Chow, J. G. Watson, L. C. Pritchett, W. R. Pierson, C. A. Frazier, and R. G. Purcell, “The DRI thermal/optical reflectance carbon analysis system: description, evaluation and applications in U.S. air quality studies,” Atmos. Environ. 27, 1185–1201 (1993).
[Crossref]

1992 (2)

L. Tsang, Z. Chen, S. Oh, and R. J. Marks, “Inversion of snow parameters from passive microwave remote sensing measurements by a neural network trained with a multiple scattering model,” IEEE Trans. Geosci. Remote Sens. GE-30, 1015–1024 (1992).
[Crossref]

J. G. Winther, “Landsat Thematic Mapper (TM) derived reflectance from a mountainous watershed during the snow melt season,” Nordic Hydrol. 23, 273–290 (1992).

1988 (1)

1980 (2)

W. J. Wiscombe and S. G. Warren, “A model for the spectral albedo of snow, I, Pure snow,” J. Atmos. Sci. 37, 2712–2733 (1980).
[Crossref]

S. G. Warren and W. J. Wiscombe, “A model for the spectral albedo of snow, II, Snow containing atmospheric aerosols,” J. Atmos. Sci. 37, 2735–2745 (1980).
[Crossref]

1974 (1)

J. E. Hansen and L. D. Travis, “Light scattering in planetary atmosphere,” Space Sci. Rev. 16, 527–610 (1974).
[Crossref]

Abdelgadir, A.

A. Abdelgadir, “Forward and inverse modeling of canopy directional reflectance using a neural network,” Int. J. Remote Sens. 19, 453–471 (1998).
[Crossref]

Abe, O.

Adachi, K.

K. Kuchiki, T. Aoki, M. Niwano, S. Matoba, Y. Kodama, and K. Adachi, “Elemental carbon, organic carbon, and dust concentrations in snow measured with thermal optical and gravimetric methods: variations during the 2007–2013 winters at Sapporo, Japan,” J. Geophys. Res. 120, 868–882 (2015).

Andreae, M. O.

M. O. Andreae and A. Gelencsér, “Black carbon or brown carbon? The nature of light-absorbing carbonaceous aerosols,” Atmos. Chem. Phys. 6, 3131–3148 (2006).
[Crossref]

Aniya, M.

T. Tanikawa, T. Aoki, M. Hori, A. Hachikubo, O. Abe, and M. Aniya, “Monte Carlo simulations of spectral albedo for artificial snowpacks composed of spherical and nonspherical particles,” Appl. Opt. 45, 5310–5319 (2006).
[Crossref] [PubMed]

T. Tanikawa, T. Aoki, M. Hori, A. Hachikubo, and M. Aniya, “Snow bidirectional reflectance model using non-spherical snow particles and its validation with field measurements,” EARSeL eProceedings 5, 137–145 (2006).

Aoki, T.

K. Kuchiki, T. Aoki, M. Niwano, S. Matoba, Y. Kodama, and K. Adachi, “Elemental carbon, organic carbon, and dust concentrations in snow measured with thermal optical and gravimetric methods: variations during the 2007–2013 winters at Sapporo, Japan,” J. Geophys. Res. 120, 868–882 (2015).

T. Tanikawa, M. Hori, T. Aoki, A. Hachikubo, K. Kuchiki, M. Niwano, S. Matoba, S. Yamaguchi, and K. Stamnes, “In situ measurements of polarization properties of snow surface under the Brewster geometry in Hokkaido, Japan and northwest Greenland ice sheet,” J. Geophys. Res. 119, 13946–13964 (2014).

N. Chen, W. Li, T. Tanikawa, M. Hori, T. Aoki, and K. Stamnes, “Cloud mask over snow-/ice-covered areas for the GCOM-C1/SGLI cryosphere mission: Validations over Greenland,” J. Geophys. Res. 119, 12287–12300 (2014).

H. Wiebe, G. Heygster, E. Zege, T. Aoki, and M. Hori, “Snow grain size retrieval SGSP from optical satellite data: Validation with ground measurements and detection of snow fall events,” Remote Sens. Environ. 128, 11–20 (2013).
[Crossref]

A. A. Kokhanovsky, V. V. Rozanov, T. Aoki, D. Odermatt, C. Brockmann, O. Krüger, M. Bouvet, M. Drusch, and M. Hori, “Sizing snow grains using backscattered solar light,” Int. J. Remote Sens. 22, 6975–7008 (2011).
[Crossref]

T. Aoki, K. Kuchiki, M. Niwano, Y. Kodama, M. Hosaka, and T. Tanaka, “Physically based snow albedo model for calculating broadband albedos and the solar heating profile in snowpack for general circulation models,” J. Geophys. Res. 116, D11114 (2011).
[Crossref]

A. Lyapustin, M. Tedesco, Y. Wang, T. Aoki, M. Hori, and A. A. Kokhanovsky, “Retrieval of snow grain size over Greenland from MODIS,” Remote Sens. Environ. 113, 976–987 (2009).
[Crossref]

K. Kuchiki, T. Aoki, T. Tanikawa, and Y. Kodama, “Retrieval of snow physical parameters using a ground-based spectral radiometer,” Appl. Opt. 48, 5567–5582 (2009).
[Crossref] [PubMed]

T. Aoki, M. Hori, H. Motoyohi, T. Tanikawa, A. Hachikubo, K. Sugiura, T. J. Yasunari, R. Storvold, H. Eide, K. Stamnes, W. Li, J. Nieke, Y. Nakajima, and F. Takahashi, “ADEOS-II/GLI snow/ice products: Part II - Validation results using GLI and MODIS data,” Remote Sens. Environ. 111, 274–290 (2007).
[Crossref]

M. Hori, T. Aoki, K. Stamnes, and W. Li, “ADEOS-II/GLI snow/ice products: Part III - Retrieved results,” Remote Sens. Environ. 111, 291–336 (2007).
[Crossref]

K. Stamnes, W. Li, H. Eide, T. Aoki, M. Hori, and R. Storvold, “ADEOS-II/GLI snow/ice products: Part I -Scientific basis,” Remote Sens. Environ. 111, 258–273 (2007).
[Crossref]

T. Tanikawa, T. Aoki, M. Hori, A. Hachikubo, O. Abe, and M. Aniya, “Monte Carlo simulations of spectral albedo for artificial snowpacks composed of spherical and nonspherical particles,” Appl. Opt. 45, 5310–5319 (2006).
[Crossref] [PubMed]

T. Tanikawa, T. Aoki, M. Hori, A. Hachikubo, and M. Aniya, “Snow bidirectional reflectance model using non-spherical snow particles and its validation with field measurements,” EARSeL eProceedings 5, 137–145 (2006).

A. A. Kokhanovsky, T. Aoki, A. Hachikubo, M. Hori, and E. P. Zege, “Reflective properties of natural snow: approximate asymptotic theory versus in situ measurements,” IEEE Trans. Geosci. Remote Sens. 43, 1529–1535 (2005).
[Crossref]

T. Aoki, A. Hachikubo, and M. Hori, “Effects of snow physical parameters on shortwave broadband albedos,” J. Geophys. Res. 108, 4616 (2003).
[Crossref]

T. Tanikawa, T. Aoki, and F. Nishio, “Remote sensing of snow grain size and snow impurities from airborne multispectral scanner data using a snow bidirectional reflectance distribution function model,” Ann. Glaciol. 34, 74–80 (2002).
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Aoki, Ta.

Te. Aoki, Ta. Aoki, M. Fukabori, A. Hachikubo, Y. Tachibana, and F. Nishio, “Effects of snow physical parameters on spectral albedo and bi-directional reflectance of snow surface,” J. Geophys. Res. 105, 10219–10236 (2000).
[Crossref]

Aoki, Te.

Te. Aoki, Ta. Aoki, M. Fukabori, A. Hachikubo, Y. Tachibana, and F. Nishio, “Effects of snow physical parameters on spectral albedo and bi-directional reflectance of snow surface,” J. Geophys. Res. 105, 10219–10236 (2000).
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Armstrong, R. L.

C. Fierz, R. L. Armstrong, Y. Durand, P. Etchevers, E. Greene, D. M. McClung, K. Nishimura, P. K. Satyawali, and S. A. Sokratov, The International Classification for Seasonal Snow on the Ground (International Association of Cryosphere Sciences, UNESCO-International Hydrological Programme, 2009).

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P. M. Atkinson and A. R. L. Tatnall, “Neural networks in remote sensing - introduction,” Int. J. Remote Sens. 18, 699–709 (1997).
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K. Stamnes, B. Hamre, J. J. Stamnes, G. Ryzhikov, M. Biryulina, R. Mahoney, B. Hauss, and A. Sei, “Modeling of radiation transport in coupled atmosphere-snow-ice-ocean systems,” J. Quant. Spectrosc. Radiat. Transfer 112, 714–726 (2011).
[Crossref]

Bohlander, J.

T. Scambos, T. Haran, M. Fahnestock, T. H. Painter, and J. Bohlander, “MODIS-based mosaic of Antarctica (MOA) data sets: Continent-wide surface morphology and snow grain size,” Remote Sens. Environ. 111, 242–257 (2007).
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M. Fily, B. Bourdelles, J. P. Dedieu, and C. Sergent, “Comparison of in situ and Landsat Thematic mapper derived snow grain characteristics in the Alps,” Remote Sens. Environ. 59, 452–460 (1997).
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Bouvet, M.

A. A. Kokhanovsky, V. V. Rozanov, T. Aoki, D. Odermatt, C. Brockmann, O. Krüger, M. Bouvet, M. Drusch, and M. Hori, “Sizing snow grains using backscattered solar light,” Int. J. Remote Sens. 22, 6975–7008 (2011).
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S. G. Warren and R. E. Brandt, “Optical constants of ice from the ultraviolet to the microwave: a revised compilation,” J. Geophys. Res. 113, D14220 (2008).
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Brockmann, C.

A. A. Kokhanovsky, V. V. Rozanov, T. Aoki, D. Odermatt, C. Brockmann, O. Krüger, M. Bouvet, M. Drusch, and M. Hori, “Sizing snow grains using backscattered solar light,” Int. J. Remote Sens. 22, 6975–7008 (2011).
[Crossref]

Charlock, T. P.

Z. Jin, T. P. Charlock, P. Yang, Y. Xie, and W. Miller, “Snow optical properties for different particle shapes with application to snow grain size retrieval and MODIS/CERES radiance comparison over Antarctica,” Remote Sens. Environ. 112, 3563–3581 (2008).
[Crossref]

Chen, B.

W. Li, K. Stamnes, and B. Chen, “Snow grain size retrieved from near-infrared radiances at multiple wavelengths,” Geophys. Res. Lett. 28, 1699–1702 (2001).
[Crossref]

Chen, J.

L. Meng, Y. He, J. Chen, and Y. Wu, “Neural network retrieval of ocean surface parameters from SSM/I data,” Mon. Weather Rev. 135, 586–597 (2007).
[Crossref]

Chen, N.

N. Chen, W. Li, T. Tanikawa, M. Hori, T. Aoki, and K. Stamnes, “Cloud mask over snow-/ice-covered areas for the GCOM-C1/SGLI cryosphere mission: Validations over Greenland,” J. Geophys. Res. 119, 12287–12300 (2014).

Chen, Z.

L. Tsang, Z. Chen, S. Oh, and R. J. Marks, “Inversion of snow parameters from passive microwave remote sensing measurements by a neural network trained with a multiple scattering model,” IEEE Trans. Geosci. Remote Sens. GE-30, 1015–1024 (1992).
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J. C. Chow, J. G. Watson, D. Crow, D. H. Lowenthal, and T. Merrifield, “Comparison of IMPROVE and NIOSH carbone measurements,” Aerosol Sci. Technol. 34, 23–34 (2001).
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J. C. Chow, J. G. Watson, L. C. Pritchett, W. R. Pierson, C. A. Frazier, and R. G. Purcell, “The DRI thermal/optical reflectance carbon analysis system: description, evaluation and applications in U.S. air quality studies,” Atmos. Environ. 27, 1185–1201 (1993).
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Crow, D.

J. C. Chow, J. G. Watson, D. Crow, D. H. Lowenthal, and T. Merrifield, “Comparison of IMPROVE and NIOSH carbone measurements,” Aerosol Sci. Technol. 34, 23–34 (2001).
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Dahlback, A.

Dedieu, J. P.

A. Mary, M. Dumont, J. P. Dedieu, Y. Durand, P. Sirguey, H. Milhem, O. Mestre, H. S. Negi, A. A. Kokhanovsky, M. Lafaysse, and S. Morin, “Intercomparison of retrieval algorithms for the specific surface area of snow from near-infrared satellite data in mountainous terrain, and comparison with the output of a semi-distributed snow-pack model,” The Cryosphere 7, 741–761 (2013).
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M. Fily, B. Bourdelles, J. P. Dedieu, and C. Sergent, “Comparison of in situ and Landsat Thematic mapper derived snow grain characteristics in the Alps,” Remote Sens. Environ. 59, 452–460 (1997).
[Crossref]

Drusch, M.

A. A. Kokhanovsky, V. V. Rozanov, T. Aoki, D. Odermatt, C. Brockmann, O. Krüger, M. Bouvet, M. Drusch, and M. Hori, “Sizing snow grains using backscattered solar light,” Int. J. Remote Sens. 22, 6975–7008 (2011).
[Crossref]

Dumont, M.

A. Mary, M. Dumont, J. P. Dedieu, Y. Durand, P. Sirguey, H. Milhem, O. Mestre, H. S. Negi, A. A. Kokhanovsky, M. Lafaysse, and S. Morin, “Intercomparison of retrieval algorithms for the specific surface area of snow from near-infrared satellite data in mountainous terrain, and comparison with the output of a semi-distributed snow-pack model,” The Cryosphere 7, 741–761 (2013).
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Durand, Y.

A. Mary, M. Dumont, J. P. Dedieu, Y. Durand, P. Sirguey, H. Milhem, O. Mestre, H. S. Negi, A. A. Kokhanovsky, M. Lafaysse, and S. Morin, “Intercomparison of retrieval algorithms for the specific surface area of snow from near-infrared satellite data in mountainous terrain, and comparison with the output of a semi-distributed snow-pack model,” The Cryosphere 7, 741–761 (2013).
[Crossref]

C. Fierz, R. L. Armstrong, Y. Durand, P. Etchevers, E. Greene, D. M. McClung, K. Nishimura, P. K. Satyawali, and S. A. Sokratov, The International Classification for Seasonal Snow on the Ground (International Association of Cryosphere Sciences, UNESCO-International Hydrological Programme, 2009).

Eide, H.

T. Aoki, M. Hori, H. Motoyohi, T. Tanikawa, A. Hachikubo, K. Sugiura, T. J. Yasunari, R. Storvold, H. Eide, K. Stamnes, W. Li, J. Nieke, Y. Nakajima, and F. Takahashi, “ADEOS-II/GLI snow/ice products: Part II - Validation results using GLI and MODIS data,” Remote Sens. Environ. 111, 274–290 (2007).
[Crossref]

K. Stamnes, W. Li, H. Eide, T. Aoki, M. Hori, and R. Storvold, “ADEOS-II/GLI snow/ice products: Part I -Scientific basis,” Remote Sens. Environ. 111, 258–273 (2007).
[Crossref]

R. Spurr, K. Stamnes, H. Eide, W. Li, K. Zhang, and J. J. Stamnes, “Simultaneous retrieval of aerosols and ocean properties: a classic inverse modeling approach. I. Analytic Jacobians from the linearized CAO-DISORT model,” J. Quantum Spectrosc. Radiat. Transfer 104, 428–449 (2007).
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Etchevers, P.

C. Fierz, R. L. Armstrong, Y. Durand, P. Etchevers, E. Greene, D. M. McClung, K. Nishimura, P. K. Satyawali, and S. A. Sokratov, The International Classification for Seasonal Snow on the Ground (International Association of Cryosphere Sciences, UNESCO-International Hydrological Programme, 2009).

Fahnestock, M.

T. Scambos, T. Haran, M. Fahnestock, T. H. Painter, and J. Bohlander, “MODIS-based mosaic of Antarctica (MOA) data sets: Continent-wide surface morphology and snow grain size,” Remote Sens. Environ. 111, 242–257 (2007).
[Crossref]

Fan, L.

Fierz, C.

C. Fierz, R. L. Armstrong, Y. Durand, P. Etchevers, E. Greene, D. M. McClung, K. Nishimura, P. K. Satyawali, and S. A. Sokratov, The International Classification for Seasonal Snow on the Ground (International Association of Cryosphere Sciences, UNESCO-International Hydrological Programme, 2009).

Fily, M.

M. Fily, B. Bourdelles, J. P. Dedieu, and C. Sergent, “Comparison of in situ and Landsat Thematic mapper derived snow grain characteristics in the Alps,” Remote Sens. Environ. 59, 452–460 (1997).
[Crossref]

Frazier, C. A.

J. C. Chow, J. G. Watson, L. C. Pritchett, W. R. Pierson, C. A. Frazier, and R. G. Purcell, “The DRI thermal/optical reflectance carbon analysis system: description, evaluation and applications in U.S. air quality studies,” Atmos. Environ. 27, 1185–1201 (1993).
[Crossref]

Fujii, H.

K. Imaoka, M. Kachi, H. Fujii, H. Murakami, M. Hori, A. Ono, T. Igarashi, K. Nakagawa, T. Oki, Y. Honda, and H. Shimoda, “Global Change Observation Mission (GCOM) for monitoring carbon, water cycles, and climate change,” Proc. IEEE 98(5), 717–734 (2010).
[Crossref]

Fukabori, M.

Te. Aoki, Ta. Aoki, M. Fukabori, A. Hachikubo, Y. Tachibana, and F. Nishio, “Effects of snow physical parameters on spectral albedo and bi-directional reflectance of snow surface,” J. Geophys. Res. 105, 10219–10236 (2000).
[Crossref]

Gelencsér, A.

M. O. Andreae and A. Gelencsér, “Black carbon or brown carbon? The nature of light-absorbing carbonaceous aerosols,” Atmos. Chem. Phys. 6, 3131–3148 (2006).
[Crossref]

Gillespie, A. R.

J. E. Kay, A. R. Gillespie, G. B. Hansen, and E. C. Pettit, “Spatial relationship between snow contaminant content, grain size, and surface temperature from multispectral images of Mt. Rainier, Washington (USA),” Remote Sens. Environ. 86, 216–231 (2003).
[Crossref]

Greene, E.

C. Fierz, R. L. Armstrong, Y. Durand, P. Etchevers, E. Greene, D. M. McClung, K. Nishimura, P. K. Satyawali, and S. A. Sokratov, The International Classification for Seasonal Snow on the Ground (International Association of Cryosphere Sciences, UNESCO-International Hydrological Programme, 2009).

Grenfell, T. C.

T. C. Grenfell and S. G. Warren, “Relationship of a nonspherical ice particle by a collection of independent spheres for scattering and absorption of radiation,” J. Geophys. Res. 104, 31697–31709 (1999).
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Hachikubo, A.

T. Tanikawa, M. Hori, T. Aoki, A. Hachikubo, K. Kuchiki, M. Niwano, S. Matoba, S. Yamaguchi, and K. Stamnes, “In situ measurements of polarization properties of snow surface under the Brewster geometry in Hokkaido, Japan and northwest Greenland ice sheet,” J. Geophys. Res. 119, 13946–13964 (2014).

T. Aoki, M. Hori, H. Motoyohi, T. Tanikawa, A. Hachikubo, K. Sugiura, T. J. Yasunari, R. Storvold, H. Eide, K. Stamnes, W. Li, J. Nieke, Y. Nakajima, and F. Takahashi, “ADEOS-II/GLI snow/ice products: Part II - Validation results using GLI and MODIS data,” Remote Sens. Environ. 111, 274–290 (2007).
[Crossref]

T. Tanikawa, T. Aoki, M. Hori, A. Hachikubo, O. Abe, and M. Aniya, “Monte Carlo simulations of spectral albedo for artificial snowpacks composed of spherical and nonspherical particles,” Appl. Opt. 45, 5310–5319 (2006).
[Crossref] [PubMed]

T. Tanikawa, T. Aoki, M. Hori, A. Hachikubo, and M. Aniya, “Snow bidirectional reflectance model using non-spherical snow particles and its validation with field measurements,” EARSeL eProceedings 5, 137–145 (2006).

A. A. Kokhanovsky, T. Aoki, A. Hachikubo, M. Hori, and E. P. Zege, “Reflective properties of natural snow: approximate asymptotic theory versus in situ measurements,” IEEE Trans. Geosci. Remote Sens. 43, 1529–1535 (2005).
[Crossref]

T. Aoki, A. Hachikubo, and M. Hori, “Effects of snow physical parameters on shortwave broadband albedos,” J. Geophys. Res. 108, 4616 (2003).
[Crossref]

Te. Aoki, Ta. Aoki, M. Fukabori, A. Hachikubo, Y. Tachibana, and F. Nishio, “Effects of snow physical parameters on spectral albedo and bi-directional reflectance of snow surface,” J. Geophys. Res. 105, 10219–10236 (2000).
[Crossref]

Hamre, B.

K. Stamnes, B. Hamre, J. J. Stamnes, G. Ryzhikov, M. Biryulina, R. Mahoney, B. Hauss, and A. Sei, “Modeling of radiation transport in coupled atmosphere-snow-ice-ocean systems,” J. Quant. Spectrosc. Radiat. Transfer 112, 714–726 (2011).
[Crossref]

Hansen, G. B.

J. E. Kay, A. R. Gillespie, G. B. Hansen, and E. C. Pettit, “Spatial relationship between snow contaminant content, grain size, and surface temperature from multispectral images of Mt. Rainier, Washington (USA),” Remote Sens. Environ. 86, 216–231 (2003).
[Crossref]

Hansen, J.

J. Hansen and L. Nazarenko, “Soot climate forcing via snow and ice albedos,” Proc. Natl. Acad. Sci. USA 101, 423–428 (2004).
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J. E. Hansen and L. D. Travis, “Light scattering in planetary atmosphere,” Space Sci. Rev. 16, 527–610 (1974).
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Haran, T.

T. Scambos, T. Haran, M. Fahnestock, T. H. Painter, and J. Bohlander, “MODIS-based mosaic of Antarctica (MOA) data sets: Continent-wide surface morphology and snow grain size,” Remote Sens. Environ. 111, 242–257 (2007).
[Crossref]

Hauss, B.

K. Stamnes, B. Hamre, J. J. Stamnes, G. Ryzhikov, M. Biryulina, R. Mahoney, B. Hauss, and A. Sei, “Modeling of radiation transport in coupled atmosphere-snow-ice-ocean systems,” J. Quant. Spectrosc. Radiat. Transfer 112, 714–726 (2011).
[Crossref]

He, Y.

L. Meng, Y. He, J. Chen, and Y. Wu, “Neural network retrieval of ocean surface parameters from SSM/I data,” Mon. Weather Rev. 135, 586–597 (2007).
[Crossref]

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M. Hess, P. Koepke, and I. Schult, “Optical properties of aerosols and clouds: the software package OPAC,” Bull. Am. Meteorol. Soc. 79, 831–844 (1998).
[Crossref]

Heygster, G.

H. Wiebe, G. Heygster, E. Zege, T. Aoki, and M. Hori, “Snow grain size retrieval SGSP from optical satellite data: Validation with ground measurements and detection of snow fall events,” Remote Sens. Environ. 128, 11–20 (2013).
[Crossref]

Honda, Y.

K. Imaoka, M. Kachi, H. Fujii, H. Murakami, M. Hori, A. Ono, T. Igarashi, K. Nakagawa, T. Oki, Y. Honda, and H. Shimoda, “Global Change Observation Mission (GCOM) for monitoring carbon, water cycles, and climate change,” Proc. IEEE 98(5), 717–734 (2010).
[Crossref]

Hori, M.

N. Chen, W. Li, T. Tanikawa, M. Hori, T. Aoki, and K. Stamnes, “Cloud mask over snow-/ice-covered areas for the GCOM-C1/SGLI cryosphere mission: Validations over Greenland,” J. Geophys. Res. 119, 12287–12300 (2014).

T. Tanikawa, M. Hori, T. Aoki, A. Hachikubo, K. Kuchiki, M. Niwano, S. Matoba, S. Yamaguchi, and K. Stamnes, “In situ measurements of polarization properties of snow surface under the Brewster geometry in Hokkaido, Japan and northwest Greenland ice sheet,” J. Geophys. Res. 119, 13946–13964 (2014).

H. Wiebe, G. Heygster, E. Zege, T. Aoki, and M. Hori, “Snow grain size retrieval SGSP from optical satellite data: Validation with ground measurements and detection of snow fall events,” Remote Sens. Environ. 128, 11–20 (2013).
[Crossref]

A. A. Kokhanovsky, V. V. Rozanov, T. Aoki, D. Odermatt, C. Brockmann, O. Krüger, M. Bouvet, M. Drusch, and M. Hori, “Sizing snow grains using backscattered solar light,” Int. J. Remote Sens. 22, 6975–7008 (2011).
[Crossref]

K. Imaoka, M. Kachi, H. Fujii, H. Murakami, M. Hori, A. Ono, T. Igarashi, K. Nakagawa, T. Oki, Y. Honda, and H. Shimoda, “Global Change Observation Mission (GCOM) for monitoring carbon, water cycles, and climate change,” Proc. IEEE 98(5), 717–734 (2010).
[Crossref]

A. Lyapustin, M. Tedesco, Y. Wang, T. Aoki, M. Hori, and A. A. Kokhanovsky, “Retrieval of snow grain size over Greenland from MODIS,” Remote Sens. Environ. 113, 976–987 (2009).
[Crossref]

T. Aoki, M. Hori, H. Motoyohi, T. Tanikawa, A. Hachikubo, K. Sugiura, T. J. Yasunari, R. Storvold, H. Eide, K. Stamnes, W. Li, J. Nieke, Y. Nakajima, and F. Takahashi, “ADEOS-II/GLI snow/ice products: Part II - Validation results using GLI and MODIS data,” Remote Sens. Environ. 111, 274–290 (2007).
[Crossref]

M. Hori, T. Aoki, K. Stamnes, and W. Li, “ADEOS-II/GLI snow/ice products: Part III - Retrieved results,” Remote Sens. Environ. 111, 291–336 (2007).
[Crossref]

K. Stamnes, W. Li, H. Eide, T. Aoki, M. Hori, and R. Storvold, “ADEOS-II/GLI snow/ice products: Part I -Scientific basis,” Remote Sens. Environ. 111, 258–273 (2007).
[Crossref]

T. Tanikawa, T. Aoki, M. Hori, A. Hachikubo, O. Abe, and M. Aniya, “Monte Carlo simulations of spectral albedo for artificial snowpacks composed of spherical and nonspherical particles,” Appl. Opt. 45, 5310–5319 (2006).
[Crossref] [PubMed]

T. Tanikawa, T. Aoki, M. Hori, A. Hachikubo, and M. Aniya, “Snow bidirectional reflectance model using non-spherical snow particles and its validation with field measurements,” EARSeL eProceedings 5, 137–145 (2006).

A. A. Kokhanovsky, T. Aoki, A. Hachikubo, M. Hori, and E. P. Zege, “Reflective properties of natural snow: approximate asymptotic theory versus in situ measurements,” IEEE Trans. Geosci. Remote Sens. 43, 1529–1535 (2005).
[Crossref]

T. Aoki, A. Hachikubo, and M. Hori, “Effects of snow physical parameters on shortwave broadband albedos,” J. Geophys. Res. 108, 4616 (2003).
[Crossref]

Hosaka, M.

T. Aoki, K. Kuchiki, M. Niwano, Y. Kodama, M. Hosaka, and T. Tanaka, “Physically based snow albedo model for calculating broadband albedos and the solar heating profile in snowpack for general circulation models,” J. Geophys. Res. 116, D11114 (2011).
[Crossref]

Igarashi, T.

K. Imaoka, M. Kachi, H. Fujii, H. Murakami, M. Hori, A. Ono, T. Igarashi, K. Nakagawa, T. Oki, Y. Honda, and H. Shimoda, “Global Change Observation Mission (GCOM) for monitoring carbon, water cycles, and climate change,” Proc. IEEE 98(5), 717–734 (2010).
[Crossref]

Imaoka, K.

K. Imaoka, M. Kachi, H. Fujii, H. Murakami, M. Hori, A. Ono, T. Igarashi, K. Nakagawa, T. Oki, Y. Honda, and H. Shimoda, “Global Change Observation Mission (GCOM) for monitoring carbon, water cycles, and climate change,” Proc. IEEE 98(5), 717–734 (2010).
[Crossref]

Jayaweera, K.

Jin, Z.

Z. Jin, T. P. Charlock, P. Yang, Y. Xie, and W. Miller, “Snow optical properties for different particle shapes with application to snow grain size retrieval and MODIS/CERES radiance comparison over Antarctica,” Remote Sens. Environ. 112, 3563–3581 (2008).
[Crossref]

Kachi, M.

K. Imaoka, M. Kachi, H. Fujii, H. Murakami, M. Hori, A. Ono, T. Igarashi, K. Nakagawa, T. Oki, Y. Honda, and H. Shimoda, “Global Change Observation Mission (GCOM) for monitoring carbon, water cycles, and climate change,” Proc. IEEE 98(5), 717–734 (2010).
[Crossref]

Kay, J. E.

J. E. Kay, A. R. Gillespie, G. B. Hansen, and E. C. Pettit, “Spatial relationship between snow contaminant content, grain size, and surface temperature from multispectral images of Mt. Rainier, Washington (USA),” Remote Sens. Environ. 86, 216–231 (2003).
[Crossref]

Kodama, Y.

K. Kuchiki, T. Aoki, M. Niwano, S. Matoba, Y. Kodama, and K. Adachi, “Elemental carbon, organic carbon, and dust concentrations in snow measured with thermal optical and gravimetric methods: variations during the 2007–2013 winters at Sapporo, Japan,” J. Geophys. Res. 120, 868–882 (2015).

T. Aoki, K. Kuchiki, M. Niwano, Y. Kodama, M. Hosaka, and T. Tanaka, “Physically based snow albedo model for calculating broadband albedos and the solar heating profile in snowpack for general circulation models,” J. Geophys. Res. 116, D11114 (2011).
[Crossref]

K. Kuchiki, T. Aoki, T. Tanikawa, and Y. Kodama, “Retrieval of snow physical parameters using a ground-based spectral radiometer,” Appl. Opt. 48, 5567–5582 (2009).
[Crossref] [PubMed]

Koepke, P.

M. Hess, P. Koepke, and I. Schult, “Optical properties of aerosols and clouds: the software package OPAC,” Bull. Am. Meteorol. Soc. 79, 831–844 (1998).
[Crossref]

Kokhanovsky, A. A.

A. Mary, M. Dumont, J. P. Dedieu, Y. Durand, P. Sirguey, H. Milhem, O. Mestre, H. S. Negi, A. A. Kokhanovsky, M. Lafaysse, and S. Morin, “Intercomparison of retrieval algorithms for the specific surface area of snow from near-infrared satellite data in mountainous terrain, and comparison with the output of a semi-distributed snow-pack model,” The Cryosphere 7, 741–761 (2013).
[Crossref]

A. A. Kokhanovsky, V. V. Rozanov, T. Aoki, D. Odermatt, C. Brockmann, O. Krüger, M. Bouvet, M. Drusch, and M. Hori, “Sizing snow grains using backscattered solar light,” Int. J. Remote Sens. 22, 6975–7008 (2011).
[Crossref]

A. Lyapustin, M. Tedesco, Y. Wang, T. Aoki, M. Hori, and A. A. Kokhanovsky, “Retrieval of snow grain size over Greenland from MODIS,” Remote Sens. Environ. 113, 976–987 (2009).
[Crossref]

M. Tedesco and A. A. Kokhanovsky, “The semi-analytical snow retrieval algorithm and its application to MODIS data,” Remote Sens. Environ. 111, 228–241 (2007).
[Crossref]

A. A. Kokhanovsky, T. Aoki, A. Hachikubo, M. Hori, and E. P. Zege, “Reflective properties of natural snow: approximate asymptotic theory versus in situ measurements,” IEEE Trans. Geosci. Remote Sens. 43, 1529–1535 (2005).
[Crossref]

Krüger, O.

A. A. Kokhanovsky, V. V. Rozanov, T. Aoki, D. Odermatt, C. Brockmann, O. Krüger, M. Bouvet, M. Drusch, and M. Hori, “Sizing snow grains using backscattered solar light,” Int. J. Remote Sens. 22, 6975–7008 (2011).
[Crossref]

Kuchiki, K.

K. Kuchiki, T. Aoki, M. Niwano, S. Matoba, Y. Kodama, and K. Adachi, “Elemental carbon, organic carbon, and dust concentrations in snow measured with thermal optical and gravimetric methods: variations during the 2007–2013 winters at Sapporo, Japan,” J. Geophys. Res. 120, 868–882 (2015).

T. Tanikawa, M. Hori, T. Aoki, A. Hachikubo, K. Kuchiki, M. Niwano, S. Matoba, S. Yamaguchi, and K. Stamnes, “In situ measurements of polarization properties of snow surface under the Brewster geometry in Hokkaido, Japan and northwest Greenland ice sheet,” J. Geophys. Res. 119, 13946–13964 (2014).

T. Aoki, K. Kuchiki, M. Niwano, Y. Kodama, M. Hosaka, and T. Tanaka, “Physically based snow albedo model for calculating broadband albedos and the solar heating profile in snowpack for general circulation models,” J. Geophys. Res. 116, D11114 (2011).
[Crossref]

K. Kuchiki, T. Aoki, T. Tanikawa, and Y. Kodama, “Retrieval of snow physical parameters using a ground-based spectral radiometer,” Appl. Opt. 48, 5567–5582 (2009).
[Crossref] [PubMed]

Lafaysse, M.

A. Mary, M. Dumont, J. P. Dedieu, Y. Durand, P. Sirguey, H. Milhem, O. Mestre, H. S. Negi, A. A. Kokhanovsky, M. Lafaysse, and S. Morin, “Intercomparison of retrieval algorithms for the specific surface area of snow from near-infrared satellite data in mountainous terrain, and comparison with the output of a semi-distributed snow-pack model,” The Cryosphere 7, 741–761 (2013).
[Crossref]

Li, W.

N. Chen, W. Li, T. Tanikawa, M. Hori, T. Aoki, and K. Stamnes, “Cloud mask over snow-/ice-covered areas for the GCOM-C1/SGLI cryosphere mission: Validations over Greenland,” J. Geophys. Res. 119, 12287–12300 (2014).

L. Fan, W. Li, A. Dahlback, J. J. Stamnes, S. Stamnes, and K. Stamnes, “New neural-network-based method to infer total ozone column amounts and cloud effects from multi-channel, moderate bandwidth filter instruments,” Opt. Express 22, 19595–19609 (2014).
[Crossref] [PubMed]

W. Li, K. Stamnes, R. Spurr, and J. J. Stamnes, “Simultaneous retrieval of aerosol and ocean properties by optimal estimation: SeaWiFS case studies for the Santa Barbara Channel,” Int. J. Remote Sens. 29, 5689–5698 (2008).
[Crossref]

T. Aoki, M. Hori, H. Motoyohi, T. Tanikawa, A. Hachikubo, K. Sugiura, T. J. Yasunari, R. Storvold, H. Eide, K. Stamnes, W. Li, J. Nieke, Y. Nakajima, and F. Takahashi, “ADEOS-II/GLI snow/ice products: Part II - Validation results using GLI and MODIS data,” Remote Sens. Environ. 111, 274–290 (2007).
[Crossref]

K. Stamnes, W. Li, H. Eide, T. Aoki, M. Hori, and R. Storvold, “ADEOS-II/GLI snow/ice products: Part I -Scientific basis,” Remote Sens. Environ. 111, 258–273 (2007).
[Crossref]

M. Hori, T. Aoki, K. Stamnes, and W. Li, “ADEOS-II/GLI snow/ice products: Part III - Retrieved results,” Remote Sens. Environ. 111, 291–336 (2007).
[Crossref]

R. Spurr, K. Stamnes, H. Eide, W. Li, K. Zhang, and J. J. Stamnes, “Simultaneous retrieval of aerosols and ocean properties: a classic inverse modeling approach. I. Analytic Jacobians from the linearized CAO-DISORT model,” J. Quantum Spectrosc. Radiat. Transfer 104, 428–449 (2007).
[Crossref]

W. Li, K. Stamnes, and B. Chen, “Snow grain size retrieved from near-infrared radiances at multiple wavelengths,” Geophys. Res. Lett. 28, 1699–1702 (2001).
[Crossref]

Liang, S.

A. W. Nolin and S. Liang, “Progress in bidirectional reflectance modeling and applications for surface particulate media: snow and soils,” Remote Sens. Rev. 18, 307–342 (2000).
[Crossref]

Lowenthal, D. H.

J. C. Chow, J. G. Watson, D. Crow, D. H. Lowenthal, and T. Merrifield, “Comparison of IMPROVE and NIOSH carbone measurements,” Aerosol Sci. Technol. 34, 23–34 (2001).
[Crossref]

Lyapustin, A.

A. Lyapustin, M. Tedesco, Y. Wang, T. Aoki, M. Hori, and A. A. Kokhanovsky, “Retrieval of snow grain size over Greenland from MODIS,” Remote Sens. Environ. 113, 976–987 (2009).
[Crossref]

Mahoney, R.

K. Stamnes, B. Hamre, J. J. Stamnes, G. Ryzhikov, M. Biryulina, R. Mahoney, B. Hauss, and A. Sei, “Modeling of radiation transport in coupled atmosphere-snow-ice-ocean systems,” J. Quant. Spectrosc. Radiat. Transfer 112, 714–726 (2011).
[Crossref]

Marks, R. J.

L. Tsang, Z. Chen, S. Oh, and R. J. Marks, “Inversion of snow parameters from passive microwave remote sensing measurements by a neural network trained with a multiple scattering model,” IEEE Trans. Geosci. Remote Sens. GE-30, 1015–1024 (1992).
[Crossref]

Mary, A.

A. Mary, M. Dumont, J. P. Dedieu, Y. Durand, P. Sirguey, H. Milhem, O. Mestre, H. S. Negi, A. A. Kokhanovsky, M. Lafaysse, and S. Morin, “Intercomparison of retrieval algorithms for the specific surface area of snow from near-infrared satellite data in mountainous terrain, and comparison with the output of a semi-distributed snow-pack model,” The Cryosphere 7, 741–761 (2013).
[Crossref]

Matoba, S.

K. Kuchiki, T. Aoki, M. Niwano, S. Matoba, Y. Kodama, and K. Adachi, “Elemental carbon, organic carbon, and dust concentrations in snow measured with thermal optical and gravimetric methods: variations during the 2007–2013 winters at Sapporo, Japan,” J. Geophys. Res. 120, 868–882 (2015).

T. Tanikawa, M. Hori, T. Aoki, A. Hachikubo, K. Kuchiki, M. Niwano, S. Matoba, S. Yamaguchi, and K. Stamnes, “In situ measurements of polarization properties of snow surface under the Brewster geometry in Hokkaido, Japan and northwest Greenland ice sheet,” J. Geophys. Res. 119, 13946–13964 (2014).

Matzl, M.

M. Matzl and M. Schneebeli, “Measuring specific surface area of snow by near-infrared photography,” J. Glaciol. 52, 558–564 (2006).
[Crossref]

McClung, D. M.

C. Fierz, R. L. Armstrong, Y. Durand, P. Etchevers, E. Greene, D. M. McClung, K. Nishimura, P. K. Satyawali, and S. A. Sokratov, The International Classification for Seasonal Snow on the Ground (International Association of Cryosphere Sciences, UNESCO-International Hydrological Programme, 2009).

Meng, L.

L. Meng, Y. He, J. Chen, and Y. Wu, “Neural network retrieval of ocean surface parameters from SSM/I data,” Mon. Weather Rev. 135, 586–597 (2007).
[Crossref]

Merrifield, T.

J. C. Chow, J. G. Watson, D. Crow, D. H. Lowenthal, and T. Merrifield, “Comparison of IMPROVE and NIOSH carbone measurements,” Aerosol Sci. Technol. 34, 23–34 (2001).
[Crossref]

Mestre, O.

A. Mary, M. Dumont, J. P. Dedieu, Y. Durand, P. Sirguey, H. Milhem, O. Mestre, H. S. Negi, A. A. Kokhanovsky, M. Lafaysse, and S. Morin, “Intercomparison of retrieval algorithms for the specific surface area of snow from near-infrared satellite data in mountainous terrain, and comparison with the output of a semi-distributed snow-pack model,” The Cryosphere 7, 741–761 (2013).
[Crossref]

Milhem, H.

A. Mary, M. Dumont, J. P. Dedieu, Y. Durand, P. Sirguey, H. Milhem, O. Mestre, H. S. Negi, A. A. Kokhanovsky, M. Lafaysse, and S. Morin, “Intercomparison of retrieval algorithms for the specific surface area of snow from near-infrared satellite data in mountainous terrain, and comparison with the output of a semi-distributed snow-pack model,” The Cryosphere 7, 741–761 (2013).
[Crossref]

Miller, W.

Z. Jin, T. P. Charlock, P. Yang, Y. Xie, and W. Miller, “Snow optical properties for different particle shapes with application to snow grain size retrieval and MODIS/CERES radiance comparison over Antarctica,” Remote Sens. Environ. 112, 3563–3581 (2008).
[Crossref]

Morin, S.

A. Mary, M. Dumont, J. P. Dedieu, Y. Durand, P. Sirguey, H. Milhem, O. Mestre, H. S. Negi, A. A. Kokhanovsky, M. Lafaysse, and S. Morin, “Intercomparison of retrieval algorithms for the specific surface area of snow from near-infrared satellite data in mountainous terrain, and comparison with the output of a semi-distributed snow-pack model,” The Cryosphere 7, 741–761 (2013).
[Crossref]

Motoyohi, H.

T. Aoki, M. Hori, H. Motoyohi, T. Tanikawa, A. Hachikubo, K. Sugiura, T. J. Yasunari, R. Storvold, H. Eide, K. Stamnes, W. Li, J. Nieke, Y. Nakajima, and F. Takahashi, “ADEOS-II/GLI snow/ice products: Part II - Validation results using GLI and MODIS data,” Remote Sens. Environ. 111, 274–290 (2007).
[Crossref]

Murakami, H.

K. Imaoka, M. Kachi, H. Fujii, H. Murakami, M. Hori, A. Ono, T. Igarashi, K. Nakagawa, T. Oki, Y. Honda, and H. Shimoda, “Global Change Observation Mission (GCOM) for monitoring carbon, water cycles, and climate change,” Proc. IEEE 98(5), 717–734 (2010).
[Crossref]

Nakagawa, K.

K. Imaoka, M. Kachi, H. Fujii, H. Murakami, M. Hori, A. Ono, T. Igarashi, K. Nakagawa, T. Oki, Y. Honda, and H. Shimoda, “Global Change Observation Mission (GCOM) for monitoring carbon, water cycles, and climate change,” Proc. IEEE 98(5), 717–734 (2010).
[Crossref]

Nakajima, Y.

T. Aoki, M. Hori, H. Motoyohi, T. Tanikawa, A. Hachikubo, K. Sugiura, T. J. Yasunari, R. Storvold, H. Eide, K. Stamnes, W. Li, J. Nieke, Y. Nakajima, and F. Takahashi, “ADEOS-II/GLI snow/ice products: Part II - Validation results using GLI and MODIS data,” Remote Sens. Environ. 111, 274–290 (2007).
[Crossref]

Nazarenko, L.

J. Hansen and L. Nazarenko, “Soot climate forcing via snow and ice albedos,” Proc. Natl. Acad. Sci. USA 101, 423–428 (2004).
[Crossref]

Negi, H. S.

A. Mary, M. Dumont, J. P. Dedieu, Y. Durand, P. Sirguey, H. Milhem, O. Mestre, H. S. Negi, A. A. Kokhanovsky, M. Lafaysse, and S. Morin, “Intercomparison of retrieval algorithms for the specific surface area of snow from near-infrared satellite data in mountainous terrain, and comparison with the output of a semi-distributed snow-pack model,” The Cryosphere 7, 741–761 (2013).
[Crossref]

Nieke, J.

T. Aoki, M. Hori, H. Motoyohi, T. Tanikawa, A. Hachikubo, K. Sugiura, T. J. Yasunari, R. Storvold, H. Eide, K. Stamnes, W. Li, J. Nieke, Y. Nakajima, and F. Takahashi, “ADEOS-II/GLI snow/ice products: Part II - Validation results using GLI and MODIS data,” Remote Sens. Environ. 111, 274–290 (2007).
[Crossref]

Nishimura, K.

C. Fierz, R. L. Armstrong, Y. Durand, P. Etchevers, E. Greene, D. M. McClung, K. Nishimura, P. K. Satyawali, and S. A. Sokratov, The International Classification for Seasonal Snow on the Ground (International Association of Cryosphere Sciences, UNESCO-International Hydrological Programme, 2009).

Nishio, F.

T. Tanikawa, T. Aoki, and F. Nishio, “Remote sensing of snow grain size and snow impurities from airborne multispectral scanner data using a snow bidirectional reflectance distribution function model,” Ann. Glaciol. 34, 74–80 (2002).
[Crossref]

Te. Aoki, Ta. Aoki, M. Fukabori, A. Hachikubo, Y. Tachibana, and F. Nishio, “Effects of snow physical parameters on spectral albedo and bi-directional reflectance of snow surface,” J. Geophys. Res. 105, 10219–10236 (2000).
[Crossref]

Niwano, M.

K. Kuchiki, T. Aoki, M. Niwano, S. Matoba, Y. Kodama, and K. Adachi, “Elemental carbon, organic carbon, and dust concentrations in snow measured with thermal optical and gravimetric methods: variations during the 2007–2013 winters at Sapporo, Japan,” J. Geophys. Res. 120, 868–882 (2015).

T. Tanikawa, M. Hori, T. Aoki, A. Hachikubo, K. Kuchiki, M. Niwano, S. Matoba, S. Yamaguchi, and K. Stamnes, “In situ measurements of polarization properties of snow surface under the Brewster geometry in Hokkaido, Japan and northwest Greenland ice sheet,” J. Geophys. Res. 119, 13946–13964 (2014).

T. Aoki, K. Kuchiki, M. Niwano, Y. Kodama, M. Hosaka, and T. Tanaka, “Physically based snow albedo model for calculating broadband albedos and the solar heating profile in snowpack for general circulation models,” J. Geophys. Res. 116, D11114 (2011).
[Crossref]

Nolin, A. W.

A. W. Nolin and S. Liang, “Progress in bidirectional reflectance modeling and applications for surface particulate media: snow and soils,” Remote Sens. Rev. 18, 307–342 (2000).
[Crossref]

Odermatt, D.

A. A. Kokhanovsky, V. V. Rozanov, T. Aoki, D. Odermatt, C. Brockmann, O. Krüger, M. Bouvet, M. Drusch, and M. Hori, “Sizing snow grains using backscattered solar light,” Int. J. Remote Sens. 22, 6975–7008 (2011).
[Crossref]

Oh, S.

L. Tsang, Z. Chen, S. Oh, and R. J. Marks, “Inversion of snow parameters from passive microwave remote sensing measurements by a neural network trained with a multiple scattering model,” IEEE Trans. Geosci. Remote Sens. GE-30, 1015–1024 (1992).
[Crossref]

Oki, T.

K. Imaoka, M. Kachi, H. Fujii, H. Murakami, M. Hori, A. Ono, T. Igarashi, K. Nakagawa, T. Oki, Y. Honda, and H. Shimoda, “Global Change Observation Mission (GCOM) for monitoring carbon, water cycles, and climate change,” Proc. IEEE 98(5), 717–734 (2010).
[Crossref]

Ono, A.

K. Imaoka, M. Kachi, H. Fujii, H. Murakami, M. Hori, A. Ono, T. Igarashi, K. Nakagawa, T. Oki, Y. Honda, and H. Shimoda, “Global Change Observation Mission (GCOM) for monitoring carbon, water cycles, and climate change,” Proc. IEEE 98(5), 717–734 (2010).
[Crossref]

Painter, T. H.

T. Scambos, T. Haran, M. Fahnestock, T. H. Painter, and J. Bohlander, “MODIS-based mosaic of Antarctica (MOA) data sets: Continent-wide surface morphology and snow grain size,” Remote Sens. Environ. 111, 242–257 (2007).
[Crossref]

Pettit, E. C.

J. E. Kay, A. R. Gillespie, G. B. Hansen, and E. C. Pettit, “Spatial relationship between snow contaminant content, grain size, and surface temperature from multispectral images of Mt. Rainier, Washington (USA),” Remote Sens. Environ. 86, 216–231 (2003).
[Crossref]

Pierson, W. R.

J. C. Chow, J. G. Watson, L. C. Pritchett, W. R. Pierson, C. A. Frazier, and R. G. Purcell, “The DRI thermal/optical reflectance carbon analysis system: description, evaluation and applications in U.S. air quality studies,” Atmos. Environ. 27, 1185–1201 (1993).
[Crossref]

Pritchett, L. C.

J. C. Chow, J. G. Watson, L. C. Pritchett, W. R. Pierson, C. A. Frazier, and R. G. Purcell, “The DRI thermal/optical reflectance carbon analysis system: description, evaluation and applications in U.S. air quality studies,” Atmos. Environ. 27, 1185–1201 (1993).
[Crossref]

Purcell, R. G.

J. C. Chow, J. G. Watson, L. C. Pritchett, W. R. Pierson, C. A. Frazier, and R. G. Purcell, “The DRI thermal/optical reflectance carbon analysis system: description, evaluation and applications in U.S. air quality studies,” Atmos. Environ. 27, 1185–1201 (1993).
[Crossref]

Rodgers, C. D.

C. D. Rodgers, Inverse Methods for Atmospheric Sounding - Theory and Practice (World Scientific Publishing Co. Ple. Ltd., 2000).

Rozanov, V. V.

A. A. Kokhanovsky, V. V. Rozanov, T. Aoki, D. Odermatt, C. Brockmann, O. Krüger, M. Bouvet, M. Drusch, and M. Hori, “Sizing snow grains using backscattered solar light,” Int. J. Remote Sens. 22, 6975–7008 (2011).
[Crossref]

Ryzhikov, G.

K. Stamnes, B. Hamre, J. J. Stamnes, G. Ryzhikov, M. Biryulina, R. Mahoney, B. Hauss, and A. Sei, “Modeling of radiation transport in coupled atmosphere-snow-ice-ocean systems,” J. Quant. Spectrosc. Radiat. Transfer 112, 714–726 (2011).
[Crossref]

Satyawali, P. K.

C. Fierz, R. L. Armstrong, Y. Durand, P. Etchevers, E. Greene, D. M. McClung, K. Nishimura, P. K. Satyawali, and S. A. Sokratov, The International Classification for Seasonal Snow on the Ground (International Association of Cryosphere Sciences, UNESCO-International Hydrological Programme, 2009).

Scambos, T.

T. Scambos, T. Haran, M. Fahnestock, T. H. Painter, and J. Bohlander, “MODIS-based mosaic of Antarctica (MOA) data sets: Continent-wide surface morphology and snow grain size,” Remote Sens. Environ. 111, 242–257 (2007).
[Crossref]

Schneebeli, M.

M. Matzl and M. Schneebeli, “Measuring specific surface area of snow by near-infrared photography,” J. Glaciol. 52, 558–564 (2006).
[Crossref]

M. Schneebeli and S. A. Sokratov, “Tomography of temperature gradient metamorphism of snow and associated changes in heat conductivity,” Hydrol. Process. 18, 3655–3665 (2004).
[Crossref]

Schult, I.

M. Hess, P. Koepke, and I. Schult, “Optical properties of aerosols and clouds: the software package OPAC,” Bull. Am. Meteorol. Soc. 79, 831–844 (1998).
[Crossref]

Sei, A.

K. Stamnes, B. Hamre, J. J. Stamnes, G. Ryzhikov, M. Biryulina, R. Mahoney, B. Hauss, and A. Sei, “Modeling of radiation transport in coupled atmosphere-snow-ice-ocean systems,” J. Quant. Spectrosc. Radiat. Transfer 112, 714–726 (2011).
[Crossref]

Sergent, C.

M. Fily, B. Bourdelles, J. P. Dedieu, and C. Sergent, “Comparison of in situ and Landsat Thematic mapper derived snow grain characteristics in the Alps,” Remote Sens. Environ. 59, 452–460 (1997).
[Crossref]

Shimoda, H.

K. Imaoka, M. Kachi, H. Fujii, H. Murakami, M. Hori, A. Ono, T. Igarashi, K. Nakagawa, T. Oki, Y. Honda, and H. Shimoda, “Global Change Observation Mission (GCOM) for monitoring carbon, water cycles, and climate change,” Proc. IEEE 98(5), 717–734 (2010).
[Crossref]

Sirguey, P.

A. Mary, M. Dumont, J. P. Dedieu, Y. Durand, P. Sirguey, H. Milhem, O. Mestre, H. S. Negi, A. A. Kokhanovsky, M. Lafaysse, and S. Morin, “Intercomparison of retrieval algorithms for the specific surface area of snow from near-infrared satellite data in mountainous terrain, and comparison with the output of a semi-distributed snow-pack model,” The Cryosphere 7, 741–761 (2013).
[Crossref]

Sokratov, S. A.

M. Schneebeli and S. A. Sokratov, “Tomography of temperature gradient metamorphism of snow and associated changes in heat conductivity,” Hydrol. Process. 18, 3655–3665 (2004).
[Crossref]

C. Fierz, R. L. Armstrong, Y. Durand, P. Etchevers, E. Greene, D. M. McClung, K. Nishimura, P. K. Satyawali, and S. A. Sokratov, The International Classification for Seasonal Snow on the Ground (International Association of Cryosphere Sciences, UNESCO-International Hydrological Programme, 2009).

Spurr, R.

W. Li, K. Stamnes, R. Spurr, and J. J. Stamnes, “Simultaneous retrieval of aerosol and ocean properties by optimal estimation: SeaWiFS case studies for the Santa Barbara Channel,” Int. J. Remote Sens. 29, 5689–5698 (2008).
[Crossref]

R. Spurr, K. Stamnes, H. Eide, W. Li, K. Zhang, and J. J. Stamnes, “Simultaneous retrieval of aerosols and ocean properties: a classic inverse modeling approach. I. Analytic Jacobians from the linearized CAO-DISORT model,” J. Quantum Spectrosc. Radiat. Transfer 104, 428–449 (2007).
[Crossref]

Stamnes, J. J.

L. Fan, W. Li, A. Dahlback, J. J. Stamnes, S. Stamnes, and K. Stamnes, “New neural-network-based method to infer total ozone column amounts and cloud effects from multi-channel, moderate bandwidth filter instruments,” Opt. Express 22, 19595–19609 (2014).
[Crossref] [PubMed]

K. Stamnes, B. Hamre, J. J. Stamnes, G. Ryzhikov, M. Biryulina, R. Mahoney, B. Hauss, and A. Sei, “Modeling of radiation transport in coupled atmosphere-snow-ice-ocean systems,” J. Quant. Spectrosc. Radiat. Transfer 112, 714–726 (2011).
[Crossref]

W. Li, K. Stamnes, R. Spurr, and J. J. Stamnes, “Simultaneous retrieval of aerosol and ocean properties by optimal estimation: SeaWiFS case studies for the Santa Barbara Channel,” Int. J. Remote Sens. 29, 5689–5698 (2008).
[Crossref]

R. Spurr, K. Stamnes, H. Eide, W. Li, K. Zhang, and J. J. Stamnes, “Simultaneous retrieval of aerosols and ocean properties: a classic inverse modeling approach. I. Analytic Jacobians from the linearized CAO-DISORT model,” J. Quantum Spectrosc. Radiat. Transfer 104, 428–449 (2007).
[Crossref]

Stamnes, K.

N. Chen, W. Li, T. Tanikawa, M. Hori, T. Aoki, and K. Stamnes, “Cloud mask over snow-/ice-covered areas for the GCOM-C1/SGLI cryosphere mission: Validations over Greenland,” J. Geophys. Res. 119, 12287–12300 (2014).

T. Tanikawa, M. Hori, T. Aoki, A. Hachikubo, K. Kuchiki, M. Niwano, S. Matoba, S. Yamaguchi, and K. Stamnes, “In situ measurements of polarization properties of snow surface under the Brewster geometry in Hokkaido, Japan and northwest Greenland ice sheet,” J. Geophys. Res. 119, 13946–13964 (2014).

L. Fan, W. Li, A. Dahlback, J. J. Stamnes, S. Stamnes, and K. Stamnes, “New neural-network-based method to infer total ozone column amounts and cloud effects from multi-channel, moderate bandwidth filter instruments,” Opt. Express 22, 19595–19609 (2014).
[Crossref] [PubMed]

K. Stamnes, B. Hamre, J. J. Stamnes, G. Ryzhikov, M. Biryulina, R. Mahoney, B. Hauss, and A. Sei, “Modeling of radiation transport in coupled atmosphere-snow-ice-ocean systems,” J. Quant. Spectrosc. Radiat. Transfer 112, 714–726 (2011).
[Crossref]

W. Li, K. Stamnes, R. Spurr, and J. J. Stamnes, “Simultaneous retrieval of aerosol and ocean properties by optimal estimation: SeaWiFS case studies for the Santa Barbara Channel,” Int. J. Remote Sens. 29, 5689–5698 (2008).
[Crossref]

T. Aoki, M. Hori, H. Motoyohi, T. Tanikawa, A. Hachikubo, K. Sugiura, T. J. Yasunari, R. Storvold, H. Eide, K. Stamnes, W. Li, J. Nieke, Y. Nakajima, and F. Takahashi, “ADEOS-II/GLI snow/ice products: Part II - Validation results using GLI and MODIS data,” Remote Sens. Environ. 111, 274–290 (2007).
[Crossref]

K. Stamnes, W. Li, H. Eide, T. Aoki, M. Hori, and R. Storvold, “ADEOS-II/GLI snow/ice products: Part I -Scientific basis,” Remote Sens. Environ. 111, 258–273 (2007).
[Crossref]

M. Hori, T. Aoki, K. Stamnes, and W. Li, “ADEOS-II/GLI snow/ice products: Part III - Retrieved results,” Remote Sens. Environ. 111, 291–336 (2007).
[Crossref]

R. Spurr, K. Stamnes, H. Eide, W. Li, K. Zhang, and J. J. Stamnes, “Simultaneous retrieval of aerosols and ocean properties: a classic inverse modeling approach. I. Analytic Jacobians from the linearized CAO-DISORT model,” J. Quantum Spectrosc. Radiat. Transfer 104, 428–449 (2007).
[Crossref]

W. Li, K. Stamnes, and B. Chen, “Snow grain size retrieved from near-infrared radiances at multiple wavelengths,” Geophys. Res. Lett. 28, 1699–1702 (2001).
[Crossref]

K. Stamnes, S. C. Tsay, W. J. Wiscombe, and K. Jayaweera, “Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media,” Appl. Opt. 27, 2502–2509 (1988).
[Crossref] [PubMed]

Stamnes, S.

Storvold, R.

K. Stamnes, W. Li, H. Eide, T. Aoki, M. Hori, and R. Storvold, “ADEOS-II/GLI snow/ice products: Part I -Scientific basis,” Remote Sens. Environ. 111, 258–273 (2007).
[Crossref]

T. Aoki, M. Hori, H. Motoyohi, T. Tanikawa, A. Hachikubo, K. Sugiura, T. J. Yasunari, R. Storvold, H. Eide, K. Stamnes, W. Li, J. Nieke, Y. Nakajima, and F. Takahashi, “ADEOS-II/GLI snow/ice products: Part II - Validation results using GLI and MODIS data,” Remote Sens. Environ. 111, 274–290 (2007).
[Crossref]

Sugiura, K.

T. Aoki, M. Hori, H. Motoyohi, T. Tanikawa, A. Hachikubo, K. Sugiura, T. J. Yasunari, R. Storvold, H. Eide, K. Stamnes, W. Li, J. Nieke, Y. Nakajima, and F. Takahashi, “ADEOS-II/GLI snow/ice products: Part II - Validation results using GLI and MODIS data,” Remote Sens. Environ. 111, 274–290 (2007).
[Crossref]

Tachibana, Y.

Te. Aoki, Ta. Aoki, M. Fukabori, A. Hachikubo, Y. Tachibana, and F. Nishio, “Effects of snow physical parameters on spectral albedo and bi-directional reflectance of snow surface,” J. Geophys. Res. 105, 10219–10236 (2000).
[Crossref]

Takahashi, F.

T. Aoki, M. Hori, H. Motoyohi, T. Tanikawa, A. Hachikubo, K. Sugiura, T. J. Yasunari, R. Storvold, H. Eide, K. Stamnes, W. Li, J. Nieke, Y. Nakajima, and F. Takahashi, “ADEOS-II/GLI snow/ice products: Part II - Validation results using GLI and MODIS data,” Remote Sens. Environ. 111, 274–290 (2007).
[Crossref]

Tanaka, T.

T. Aoki, K. Kuchiki, M. Niwano, Y. Kodama, M. Hosaka, and T. Tanaka, “Physically based snow albedo model for calculating broadband albedos and the solar heating profile in snowpack for general circulation models,” J. Geophys. Res. 116, D11114 (2011).
[Crossref]

Tanikawa, T.

T. Tanikawa, M. Hori, T. Aoki, A. Hachikubo, K. Kuchiki, M. Niwano, S. Matoba, S. Yamaguchi, and K. Stamnes, “In situ measurements of polarization properties of snow surface under the Brewster geometry in Hokkaido, Japan and northwest Greenland ice sheet,” J. Geophys. Res. 119, 13946–13964 (2014).

N. Chen, W. Li, T. Tanikawa, M. Hori, T. Aoki, and K. Stamnes, “Cloud mask over snow-/ice-covered areas for the GCOM-C1/SGLI cryosphere mission: Validations over Greenland,” J. Geophys. Res. 119, 12287–12300 (2014).

K. Kuchiki, T. Aoki, T. Tanikawa, and Y. Kodama, “Retrieval of snow physical parameters using a ground-based spectral radiometer,” Appl. Opt. 48, 5567–5582 (2009).
[Crossref] [PubMed]

T. Aoki, M. Hori, H. Motoyohi, T. Tanikawa, A. Hachikubo, K. Sugiura, T. J. Yasunari, R. Storvold, H. Eide, K. Stamnes, W. Li, J. Nieke, Y. Nakajima, and F. Takahashi, “ADEOS-II/GLI snow/ice products: Part II - Validation results using GLI and MODIS data,” Remote Sens. Environ. 111, 274–290 (2007).
[Crossref]

T. Tanikawa, T. Aoki, M. Hori, A. Hachikubo, O. Abe, and M. Aniya, “Monte Carlo simulations of spectral albedo for artificial snowpacks composed of spherical and nonspherical particles,” Appl. Opt. 45, 5310–5319 (2006).
[Crossref] [PubMed]

T. Tanikawa, T. Aoki, M. Hori, A. Hachikubo, and M. Aniya, “Snow bidirectional reflectance model using non-spherical snow particles and its validation with field measurements,” EARSeL eProceedings 5, 137–145 (2006).

T. Tanikawa, T. Aoki, and F. Nishio, “Remote sensing of snow grain size and snow impurities from airborne multispectral scanner data using a snow bidirectional reflectance distribution function model,” Ann. Glaciol. 34, 74–80 (2002).
[Crossref]

Tatnall, A. R. L.

P. M. Atkinson and A. R. L. Tatnall, “Neural networks in remote sensing - introduction,” Int. J. Remote Sens. 18, 699–709 (1997).
[Crossref]

Tedesco, M.

A. Lyapustin, M. Tedesco, Y. Wang, T. Aoki, M. Hori, and A. A. Kokhanovsky, “Retrieval of snow grain size over Greenland from MODIS,” Remote Sens. Environ. 113, 976–987 (2009).
[Crossref]

M. Tedesco and A. A. Kokhanovsky, “The semi-analytical snow retrieval algorithm and its application to MODIS data,” Remote Sens. Environ. 111, 228–241 (2007).
[Crossref]

Travis, L. D.

J. E. Hansen and L. D. Travis, “Light scattering in planetary atmosphere,” Space Sci. Rev. 16, 527–610 (1974).
[Crossref]

Tsang, L.

L. Tsang, Z. Chen, S. Oh, and R. J. Marks, “Inversion of snow parameters from passive microwave remote sensing measurements by a neural network trained with a multiple scattering model,” IEEE Trans. Geosci. Remote Sens. GE-30, 1015–1024 (1992).
[Crossref]

Tsay, S. C.

Wang, Y.

A. Lyapustin, M. Tedesco, Y. Wang, T. Aoki, M. Hori, and A. A. Kokhanovsky, “Retrieval of snow grain size over Greenland from MODIS,” Remote Sens. Environ. 113, 976–987 (2009).
[Crossref]

Warren, S. G.

S. G. Warren and R. E. Brandt, “Optical constants of ice from the ultraviolet to the microwave: a revised compilation,” J. Geophys. Res. 113, D14220 (2008).
[Crossref]

T. C. Grenfell and S. G. Warren, “Relationship of a nonspherical ice particle by a collection of independent spheres for scattering and absorption of radiation,” J. Geophys. Res. 104, 31697–31709 (1999).
[Crossref]

W. J. Wiscombe and S. G. Warren, “A model for the spectral albedo of snow, I, Pure snow,” J. Atmos. Sci. 37, 2712–2733 (1980).
[Crossref]

S. G. Warren and W. J. Wiscombe, “A model for the spectral albedo of snow, II, Snow containing atmospheric aerosols,” J. Atmos. Sci. 37, 2735–2745 (1980).
[Crossref]

Watson, J. G.

J. C. Chow, J. G. Watson, D. Crow, D. H. Lowenthal, and T. Merrifield, “Comparison of IMPROVE and NIOSH carbone measurements,” Aerosol Sci. Technol. 34, 23–34 (2001).
[Crossref]

J. C. Chow, J. G. Watson, L. C. Pritchett, W. R. Pierson, C. A. Frazier, and R. G. Purcell, “The DRI thermal/optical reflectance carbon analysis system: description, evaluation and applications in U.S. air quality studies,” Atmos. Environ. 27, 1185–1201 (1993).
[Crossref]

Wiebe, H.

H. Wiebe, G. Heygster, E. Zege, T. Aoki, and M. Hori, “Snow grain size retrieval SGSP from optical satellite data: Validation with ground measurements and detection of snow fall events,” Remote Sens. Environ. 128, 11–20 (2013).
[Crossref]

Winther, J. G.

J. G. Winther, “Landsat Thematic Mapper (TM) derived reflectance from a mountainous watershed during the snow melt season,” Nordic Hydrol. 23, 273–290 (1992).

Wiscombe, W. J.

K. Stamnes, S. C. Tsay, W. J. Wiscombe, and K. Jayaweera, “Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media,” Appl. Opt. 27, 2502–2509 (1988).
[Crossref] [PubMed]

S. G. Warren and W. J. Wiscombe, “A model for the spectral albedo of snow, II, Snow containing atmospheric aerosols,” J. Atmos. Sci. 37, 2735–2745 (1980).
[Crossref]

W. J. Wiscombe and S. G. Warren, “A model for the spectral albedo of snow, I, Pure snow,” J. Atmos. Sci. 37, 2712–2733 (1980).
[Crossref]

Wu, Y.

L. Meng, Y. He, J. Chen, and Y. Wu, “Neural network retrieval of ocean surface parameters from SSM/I data,” Mon. Weather Rev. 135, 586–597 (2007).
[Crossref]

Xie, Y.

Z. Jin, T. P. Charlock, P. Yang, Y. Xie, and W. Miller, “Snow optical properties for different particle shapes with application to snow grain size retrieval and MODIS/CERES radiance comparison over Antarctica,” Remote Sens. Environ. 112, 3563–3581 (2008).
[Crossref]

Yamaguchi, S.

T. Tanikawa, M. Hori, T. Aoki, A. Hachikubo, K. Kuchiki, M. Niwano, S. Matoba, S. Yamaguchi, and K. Stamnes, “In situ measurements of polarization properties of snow surface under the Brewster geometry in Hokkaido, Japan and northwest Greenland ice sheet,” J. Geophys. Res. 119, 13946–13964 (2014).

Yang, P.

Z. Jin, T. P. Charlock, P. Yang, Y. Xie, and W. Miller, “Snow optical properties for different particle shapes with application to snow grain size retrieval and MODIS/CERES radiance comparison over Antarctica,” Remote Sens. Environ. 112, 3563–3581 (2008).
[Crossref]

Yasunari, T. J.

T. Aoki, M. Hori, H. Motoyohi, T. Tanikawa, A. Hachikubo, K. Sugiura, T. J. Yasunari, R. Storvold, H. Eide, K. Stamnes, W. Li, J. Nieke, Y. Nakajima, and F. Takahashi, “ADEOS-II/GLI snow/ice products: Part II - Validation results using GLI and MODIS data,” Remote Sens. Environ. 111, 274–290 (2007).
[Crossref]

Zege, E.

H. Wiebe, G. Heygster, E. Zege, T. Aoki, and M. Hori, “Snow grain size retrieval SGSP from optical satellite data: Validation with ground measurements and detection of snow fall events,” Remote Sens. Environ. 128, 11–20 (2013).
[Crossref]

Zege, E. P.

A. A. Kokhanovsky, T. Aoki, A. Hachikubo, M. Hori, and E. P. Zege, “Reflective properties of natural snow: approximate asymptotic theory versus in situ measurements,” IEEE Trans. Geosci. Remote Sens. 43, 1529–1535 (2005).
[Crossref]

Zhang, K.

R. Spurr, K. Stamnes, H. Eide, W. Li, K. Zhang, and J. J. Stamnes, “Simultaneous retrieval of aerosols and ocean properties: a classic inverse modeling approach. I. Analytic Jacobians from the linearized CAO-DISORT model,” J. Quantum Spectrosc. Radiat. Transfer 104, 428–449 (2007).
[Crossref]

Aerosol Sci. Technol. (1)

J. C. Chow, J. G. Watson, D. Crow, D. H. Lowenthal, and T. Merrifield, “Comparison of IMPROVE and NIOSH carbone measurements,” Aerosol Sci. Technol. 34, 23–34 (2001).
[Crossref]

Ann. Glaciol. (1)

T. Tanikawa, T. Aoki, and F. Nishio, “Remote sensing of snow grain size and snow impurities from airborne multispectral scanner data using a snow bidirectional reflectance distribution function model,” Ann. Glaciol. 34, 74–80 (2002).
[Crossref]

Appl. Opt. (3)

Atmos. Chem. Phys. (1)

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J. C. Chow, J. G. Watson, L. C. Pritchett, W. R. Pierson, C. A. Frazier, and R. G. Purcell, “The DRI thermal/optical reflectance carbon analysis system: description, evaluation and applications in U.S. air quality studies,” Atmos. Environ. 27, 1185–1201 (1993).
[Crossref]

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M. Hess, P. Koepke, and I. Schult, “Optical properties of aerosols and clouds: the software package OPAC,” Bull. Am. Meteorol. Soc. 79, 831–844 (1998).
[Crossref]

EARSeL eProceedings (1)

T. Tanikawa, T. Aoki, M. Hori, A. Hachikubo, and M. Aniya, “Snow bidirectional reflectance model using non-spherical snow particles and its validation with field measurements,” EARSeL eProceedings 5, 137–145 (2006).

Geophys. Res. Lett. (1)

W. Li, K. Stamnes, and B. Chen, “Snow grain size retrieved from near-infrared radiances at multiple wavelengths,” Geophys. Res. Lett. 28, 1699–1702 (2001).
[Crossref]

Hydrol. Process. (1)

M. Schneebeli and S. A. Sokratov, “Tomography of temperature gradient metamorphism of snow and associated changes in heat conductivity,” Hydrol. Process. 18, 3655–3665 (2004).
[Crossref]

IEEE Trans. Geosci. Remote Sens. (2)

L. Tsang, Z. Chen, S. Oh, and R. J. Marks, “Inversion of snow parameters from passive microwave remote sensing measurements by a neural network trained with a multiple scattering model,” IEEE Trans. Geosci. Remote Sens. GE-30, 1015–1024 (1992).
[Crossref]

A. A. Kokhanovsky, T. Aoki, A. Hachikubo, M. Hori, and E. P. Zege, “Reflective properties of natural snow: approximate asymptotic theory versus in situ measurements,” IEEE Trans. Geosci. Remote Sens. 43, 1529–1535 (2005).
[Crossref]

Int. J. Remote Sens. (4)

A. Abdelgadir, “Forward and inverse modeling of canopy directional reflectance using a neural network,” Int. J. Remote Sens. 19, 453–471 (1998).
[Crossref]

P. M. Atkinson and A. R. L. Tatnall, “Neural networks in remote sensing - introduction,” Int. J. Remote Sens. 18, 699–709 (1997).
[Crossref]

W. Li, K. Stamnes, R. Spurr, and J. J. Stamnes, “Simultaneous retrieval of aerosol and ocean properties by optimal estimation: SeaWiFS case studies for the Santa Barbara Channel,” Int. J. Remote Sens. 29, 5689–5698 (2008).
[Crossref]

A. A. Kokhanovsky, V. V. Rozanov, T. Aoki, D. Odermatt, C. Brockmann, O. Krüger, M. Bouvet, M. Drusch, and M. Hori, “Sizing snow grains using backscattered solar light,” Int. J. Remote Sens. 22, 6975–7008 (2011).
[Crossref]

J. Atmos. Sci. (2)

W. J. Wiscombe and S. G. Warren, “A model for the spectral albedo of snow, I, Pure snow,” J. Atmos. Sci. 37, 2712–2733 (1980).
[Crossref]

S. G. Warren and W. J. Wiscombe, “A model for the spectral albedo of snow, II, Snow containing atmospheric aerosols,” J. Atmos. Sci. 37, 2735–2745 (1980).
[Crossref]

J. Geophys. Res. (8)

T. Aoki, A. Hachikubo, and M. Hori, “Effects of snow physical parameters on shortwave broadband albedos,” J. Geophys. Res. 108, 4616 (2003).
[Crossref]

T. Aoki, K. Kuchiki, M. Niwano, Y. Kodama, M. Hosaka, and T. Tanaka, “Physically based snow albedo model for calculating broadband albedos and the solar heating profile in snowpack for general circulation models,” J. Geophys. Res. 116, D11114 (2011).
[Crossref]

K. Kuchiki, T. Aoki, M. Niwano, S. Matoba, Y. Kodama, and K. Adachi, “Elemental carbon, organic carbon, and dust concentrations in snow measured with thermal optical and gravimetric methods: variations during the 2007–2013 winters at Sapporo, Japan,” J. Geophys. Res. 120, 868–882 (2015).

T. C. Grenfell and S. G. Warren, “Relationship of a nonspherical ice particle by a collection of independent spheres for scattering and absorption of radiation,” J. Geophys. Res. 104, 31697–31709 (1999).
[Crossref]

S. G. Warren and R. E. Brandt, “Optical constants of ice from the ultraviolet to the microwave: a revised compilation,” J. Geophys. Res. 113, D14220 (2008).
[Crossref]

Te. Aoki, Ta. Aoki, M. Fukabori, A. Hachikubo, Y. Tachibana, and F. Nishio, “Effects of snow physical parameters on spectral albedo and bi-directional reflectance of snow surface,” J. Geophys. Res. 105, 10219–10236 (2000).
[Crossref]

N. Chen, W. Li, T. Tanikawa, M. Hori, T. Aoki, and K. Stamnes, “Cloud mask over snow-/ice-covered areas for the GCOM-C1/SGLI cryosphere mission: Validations over Greenland,” J. Geophys. Res. 119, 12287–12300 (2014).

T. Tanikawa, M. Hori, T. Aoki, A. Hachikubo, K. Kuchiki, M. Niwano, S. Matoba, S. Yamaguchi, and K. Stamnes, “In situ measurements of polarization properties of snow surface under the Brewster geometry in Hokkaido, Japan and northwest Greenland ice sheet,” J. Geophys. Res. 119, 13946–13964 (2014).

J. Glaciol. (1)

M. Matzl and M. Schneebeli, “Measuring specific surface area of snow by near-infrared photography,” J. Glaciol. 52, 558–564 (2006).
[Crossref]

J. Quant. Spectrosc. Radiat. Transfer (1)

K. Stamnes, B. Hamre, J. J. Stamnes, G. Ryzhikov, M. Biryulina, R. Mahoney, B. Hauss, and A. Sei, “Modeling of radiation transport in coupled atmosphere-snow-ice-ocean systems,” J. Quant. Spectrosc. Radiat. Transfer 112, 714–726 (2011).
[Crossref]

J. Quantum Spectrosc. Radiat. Transfer (1)

R. Spurr, K. Stamnes, H. Eide, W. Li, K. Zhang, and J. J. Stamnes, “Simultaneous retrieval of aerosols and ocean properties: a classic inverse modeling approach. I. Analytic Jacobians from the linearized CAO-DISORT model,” J. Quantum Spectrosc. Radiat. Transfer 104, 428–449 (2007).
[Crossref]

Mon. Weather Rev. (1)

L. Meng, Y. He, J. Chen, and Y. Wu, “Neural network retrieval of ocean surface parameters from SSM/I data,” Mon. Weather Rev. 135, 586–597 (2007).
[Crossref]

Nordic Hydrol. (1)

J. G. Winther, “Landsat Thematic Mapper (TM) derived reflectance from a mountainous watershed during the snow melt season,” Nordic Hydrol. 23, 273–290 (1992).

Opt. Express (1)

Proc. IEEE (1)

K. Imaoka, M. Kachi, H. Fujii, H. Murakami, M. Hori, A. Ono, T. Igarashi, K. Nakagawa, T. Oki, Y. Honda, and H. Shimoda, “Global Change Observation Mission (GCOM) for monitoring carbon, water cycles, and climate change,” Proc. IEEE 98(5), 717–734 (2010).
[Crossref]

Proc. Natl. Acad. Sci. USA (1)

J. Hansen and L. Nazarenko, “Soot climate forcing via snow and ice albedos,” Proc. Natl. Acad. Sci. USA 101, 423–428 (2004).
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Remote Sens. Environ. (10)

T. Aoki, M. Hori, H. Motoyohi, T. Tanikawa, A. Hachikubo, K. Sugiura, T. J. Yasunari, R. Storvold, H. Eide, K. Stamnes, W. Li, J. Nieke, Y. Nakajima, and F. Takahashi, “ADEOS-II/GLI snow/ice products: Part II - Validation results using GLI and MODIS data,” Remote Sens. Environ. 111, 274–290 (2007).
[Crossref]

M. Tedesco and A. A. Kokhanovsky, “The semi-analytical snow retrieval algorithm and its application to MODIS data,” Remote Sens. Environ. 111, 228–241 (2007).
[Crossref]

T. Scambos, T. Haran, M. Fahnestock, T. H. Painter, and J. Bohlander, “MODIS-based mosaic of Antarctica (MOA) data sets: Continent-wide surface morphology and snow grain size,” Remote Sens. Environ. 111, 242–257 (2007).
[Crossref]

Z. Jin, T. P. Charlock, P. Yang, Y. Xie, and W. Miller, “Snow optical properties for different particle shapes with application to snow grain size retrieval and MODIS/CERES radiance comparison over Antarctica,” Remote Sens. Environ. 112, 3563–3581 (2008).
[Crossref]

K. Stamnes, W. Li, H. Eide, T. Aoki, M. Hori, and R. Storvold, “ADEOS-II/GLI snow/ice products: Part I -Scientific basis,” Remote Sens. Environ. 111, 258–273 (2007).
[Crossref]

A. Lyapustin, M. Tedesco, Y. Wang, T. Aoki, M. Hori, and A. A. Kokhanovsky, “Retrieval of snow grain size over Greenland from MODIS,” Remote Sens. Environ. 113, 976–987 (2009).
[Crossref]

H. Wiebe, G. Heygster, E. Zege, T. Aoki, and M. Hori, “Snow grain size retrieval SGSP from optical satellite data: Validation with ground measurements and detection of snow fall events,” Remote Sens. Environ. 128, 11–20 (2013).
[Crossref]

M. Hori, T. Aoki, K. Stamnes, and W. Li, “ADEOS-II/GLI snow/ice products: Part III - Retrieved results,” Remote Sens. Environ. 111, 291–336 (2007).
[Crossref]

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Remote Sens. Rev. (1)

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The Cryosphere (1)

A. Mary, M. Dumont, J. P. Dedieu, Y. Durand, P. Sirguey, H. Milhem, O. Mestre, H. S. Negi, A. A. Kokhanovsky, M. Lafaysse, and S. Morin, “Intercomparison of retrieval algorithms for the specific surface area of snow from near-infrared satellite data in mountainous terrain, and comparison with the output of a semi-distributed snow-pack model,” The Cryosphere 7, 741–761 (2013).
[Crossref]

Other (4)

AVIRIS homepage, http://aviris.jpl.nasa.gov/links/index.html

AMSS homepage, http://sharaku.eorc.jaxa.jp/ADEOS2/COMMON/AMSS/index.html

C. D. Rodgers, Inverse Methods for Atmospheric Sounding - Theory and Practice (World Scientific Publishing Co. Ple. Ltd., 2000).

C. Fierz, R. L. Armstrong, Y. Durand, P. Etchevers, E. Greene, D. M. McClung, K. Nishimura, P. K. Satyawali, and S. A. Sokratov, The International Classification for Seasonal Snow on the Ground (International Association of Cryosphere Sciences, UNESCO-International Hydrological Programme, 2009).

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Figures (8)

Fig. 1
Fig. 1

Conceptual illustration of snow retrieval algorithm. The RBF-NN is trained as the forward and inverse NN function, respectively, based on a large data set of {P,R} computed by the DISORT model. Then, the non-linear optimization loop did the retrieval. Ymeas is set to the measurement data and the solar zenith angle as input data. The vector x ^ contains the retrieved snow parameters.

Fig. 2
Fig. 2

Comparison of spectral albedo derived by the forward NN function R = mNN(P) with those of the reference data set {R}. R2 and RMSE are a determination coefficient and a root mean square error, respectively.

Fig. 3
Fig. 3

(top) Comparison of the first guess x0 of snow parameters derived by the inverse NN function P = m NN 1 ( R ) with those by the reference data set {P}, and (bottom) comparison of retrieved snow parameters x ^ with those by the reference data set {P}. Color bar is the relative error for each point in the scatter plot, which is [(Px0)/P] ×100 for the first guess (top), and [ ( P x ^ ) / P ] × 100 for the retrieved parameter (bottom). Unit of x- and y-axis is μm for rtop and rsub, and ppmw for cimp. R2 and RMSE are the determination coefficient and the root mean square error, respectively.

Fig. 4
Fig. 4

Photographs show GSAF instrument and three measurement modes [38]. (a) The GSAF was mounted at a height of 1.8 m above the ground surface. (b) The diffuse component of the downward flux is measured with the shadow blade blocking the direct component. The downward global (upward) radiant flux is measured by turning the sensor unit upward (downward); (c) global mode and (d) upward mode. (e) Schematic illustration of the GSAF.

Fig. 5
Fig. 5

Snow albedo measurements at Sapporo [(a) and (b)] and Memuro [(c) and (d)] during two winters of 2007–2008 [(a) and (c)] and 2008–2009 [(b) and (d)]. These measured values are 30 min averages from 1131 to 1200 h local time, around local solar noon. There are no data available during the period marked by arrows. The snow depth data are also plotted in each figure.

Fig. 6
Fig. 6

Daily variations of snow grain size and snow impurity concentration measured in the two winter season 2007–2008 and 2008–2009 and those retrieved by the non-linear optimal estimation method; Sapporo site [(a) and (b)], and Memuro site [(c) and (d)]. r ^ top and r ^ sub are retrieved topmost- and subsurface-grain size, respectively. r 2 sfc . 1 is the in-situ measured snow grain radius at a snow surface (d = 0 − 1 cm depth) and r 2 sub : 1 3 is the same but averaged in 1 to 3 cm layer. The upper and lower extents of r2-error bar represent the maximum and minimum of the in-situ measured snow grain radius, respectively. ĉimp is retrieved snow impurity. c eq . BC sfc . 2 are in-situ measured the BC-equivalent impurity concentration for d = 0 − 2 cm depth. The upper extent of c eq . BC sfc . 2 -error bar represents the concentration of dust c dust sfc . 2 , whereas the lower extent is the concentration of EC c EC sfc . 2 for d = 0 − 2 cm depth obtained in the filtering and the carbon analyses. There are no in-situ data available at Memuro in 2008/09 winter seasion.

Fig. 7
Fig. 7

Relationship between retrieved snow grain size and in situ measured one: (a) topmost-layer grain size r ^ top versus in-situ measured depth-averaged grain size r 2 sfc . 1 and (b) subsurface-layer snow grain size r ^ sub versus r 2 sub : 1 3 . The solid line represents a 1:1 relationship. R2 is the determination coefficient. In Fig. (a), two open circles are for r 2 sfc . 1 1000 μm.

Fig. 8
Fig. 8

Relationship between retrieved mass concentration ĉimp and in situ measured BC-equivalent mass concentration of snow impurity ceq.BC. (a) The snow layers of the in situ measurements are 0 to 2 cm (bullet) and 0 to 10 cm (open circle), and (b) 0 to 2 cm (bullet) when r ^ top 80 μm and 0 to 10 cm (open circle) when r ^ top > 80 μm. The solid line represents a 1:1 relationship. R2 is the determination coefficient.

Tables (1)

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Table 1 Summary of statistical analysis between retrieved snow physical parameters and in situ measurements.

Equations (6)

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R i = j = 1 N a i j exp { b 2 k = 1 N p ( P k c j k ) 2 } + d i ,
J i k = R i P k = 2 j = 1 N a i j b 2 ( P k c j k ) exp { b 2 l = 1 N p ( P l c j l ) 2 } .
P k = j = 1 N a k j exp { f 2 i = 1 N r ( R i g j i ) 2 } + h k ,
x i + 1 = x a + G i [ Y meas F ( x i , b ) + K i ( x i x a ) ] ,
G i = S a K i T ( K i S a K i T + S ε ) 1 .
c eq . BC = c EC k a BC + c dust k a dust k a BC ,

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