Scalar arguments of the mathematical functions defining molecular and turbulent transport of heat and mass in compressible fluids

Andrew S. Kowalski; Daniel Argüeso

doi:10.1111/j.1600-0889.2011.00579.x

Authors:

Andrew S. Kowalski ,

Departamento de Física Aplicada, Facultad de Ciencias, Universidad de Granada; Centro Andaluz de Medio Ambiente (CEAMA), ES

Daniel Argüeso

Departamento de Física Aplicada, Facultad de Ciencias, Universidad de Granada, ES

Abstract

The advection–diffusion equations defining control volume conservation laws in micrometeorological research are analysed to resolve discrepancies in their appropriate scalar variables for heat and mass transport. A scalar variable that is conserved during vertical motions enables the interpretation of turbulent mixing as ‘diffusion’. Gas-phase heat advection is shown to depend on gradients in the potential temperature (θ), not the temperature (T). Since conduction and radiation depend on T, advection–diffusion of heat depends on gradients of both θ and T. Conservation of θ (the first Law of Thermodynamics) requires including a pressure covariance term in the definition of the turbulent heat flux. Mass advection and diffusion are universally agreed to depend directly on gradients in the gas ‘concentration’ (c), a nonetheless ambiguous term. Depending upon author, c may be defined either as a dimensionless proportion or as a dimensional density, with non-trivial differences for the gas phase. Analyses of atmospheric law, scalar conservation and similarity theory demonstrate that mass advection–diffusion in gases depends on gradients, not in density but rather in a conserved proportion. Flux-tower researchers are encouraged to respect the meteorological tradition of writing conservation equations in terms of scalar variables that are conserved through simple air motions

How to Cite: Kowalski, A.S. and Argüeso, D., 2011. Scalar arguments of the mathematical functions defining molecular and turbulent transport of heat and mass in compressible fluids. Tellus B: Chemical and Physical Meteorology, 63(5), pp.1059–1066. DOI: http://doi.org/10.1111/j.1600-0889.2011.00579.x

Accepted on 21 Jul 2011 Submitted on 4 Dec 2010

References

Arya , S. P . 1988 . Introduction to Micrometeorology . Academic Press , San Diego .

Baldocchi , D . 2008 . Breathing of the terrestrial biosphere: lessons learned from a global network of carbon dioxide flux measurement systems . Australian J. Bot . 56 , 1 – 26 .

Baldocchi , D. D. , Hicks , B. B. and Meyers , T. P . 1988 . Measuring biosphere-atmosphere exchange of biologically-related gases with micrometeorological methods . Ecology 69 , 1331 – 1340 .

Barenblatt , G.I . 2003 . Scaling . Cambridge University Press , Cambridge .

Batchelor , G. K . 1967 . An Introduction to Fluid Dynamics . Cambridge University Press , Cambridge .

Betts , A. K. and Albrecht , B. A . 1986 . Conserved variable analysis of the convective boundary layer thermodynamic structure over the tropical oceans. J. Atmos. Sci . 44 , 83 – 99 .

Bird , R. B. , Stewart , W. E. and Lightfoot , E. N . 2002 . Transport Phe-nomena . John Wiley & Sons , Cambridge .

Bres , M. and Hatzfeld , C . 1977 . Three-gas diffusion: experimental and theoretical study . Eur. J. PhysioL 371 , 227 – 233 .

Buckingham , E . 1914 . On physically similar systems: illustrations of the use of dimensional equations . Phys. Rev . 4 , 345 – 376 .

Businger , J. A . 1986 . Evaluation of the accuracy with which dry depo-sition can be measured with current micrometeorological techniques . J. Clim. AppL Meteorol . 25 , 1100 – 1124 .

Businger , J. A. and Yaglom , A. M . 1971 . Introduction to Obulchov's paper on ‘Turbulence in an atmosphere with a non-uniform tempera-ture’ . Bound.-Layer MeteoroL 2 , 3 – 6 .

Campbell , G. S. and Norman , J. M . 1998 . Environmental Biophysics . Springer-Verlag , New York .

Davidson , E. A. and Trumbore , S. E . 1995 . Gas diffusivity and pro-duction of CO2 in the deep soils of the eastern Amazon . Tellus 47B , 550 – 565 .

Fierer , N. , Chadwick , O. A. and Trumbore , S. E . 2005 . Production of CO2 in soil profiles of a California annual grassland . Ecosystems 8 , 412 – 429 .

Finnigan , J. J . 2004 . A re-evaluation of long-term flux measurement techniques. Part II: Coordinate systems . Bound.-Layer MeteoroL 113 , 1 – 41 .

Finnigan , J . 2008 . An introduction to flux measurements in difficult conditions . EcoL Appl . 18 , 1340 – 1350 .

Finnigan , J. J . 2009 . Response to comment by Dr. A.S. Kowalski on “The storage term in eddy flux calculations” . Agri. Forest MeteoroL 149 , 725 – 729 .

Finnigan , J. J. , Clement , R. , Malhi , Y. , Leuning , R. and Cleugh , H. A . 2003 . A re-evaluation of long-term flux measurement techniques. Part I: averaging and coordinate rotation . Bound.-Layer MeteoroL 107 , 1 – 48 .

Foken , T . 2008 . Micrometeorology . Springer-Verlag , Berlin Heidelberg .

Font , A. , Morgui , J.-A. , Curcoll , R. , Pouchet , I. , Caals , I. and co-authors . 2010 . Daily carbon surface fluxes in theWest Ebre (Ebro) watershed from aircraft profiling on late June 2007. Tellus 62B , 427 - 440 .

Forster , P. , Ramaswamy , V , Artaxo , P. , Berntsen , N. L. , Betts , R. and co-authors . 2007 . Changes in atmospheric constituents and in radia-tive forcing. In: Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change eds. Solomon, S. , D. Qin , M. Manning , Z. Chen , M. Marquis et al.). Cambridge University Press , Cambridge, United Kingdom and New York, NY, USA .

van Gorsel , E. , Leuning , R. , Cleugh , H. A. , Keith , H. and Suni , T . 2007 . Nocturnal carbon efflux: reconciliation of eddy covariance and cham-ber measurements using an alternative to the u*-threshold filtering technique . Tellus 59B , 397 – 403 .

Ha , K.-J. and Mahrt , L . 2003 . Radiative and turbulent fluxes in the nocturnal boundary layer . Tellus 55A , 317 – 327 .

Holton , J. R . 1992 . An Introduction to Dynamic Meteorology . Academic Press , San Diego .

Kaimal , J. C. and Finnigan , J. J . 1994 . Atmospheric Boundary Layer Flows Their Measurement and Structure . Oxford University Press , New York .

Katul , G. G. , Finkelstein , P. L. , Clarke , J. E and Ellestad , T. G . 1996 . An investigation of the conditional sampling method used to estimate fluxes of active, reactive, and passive scalars . J. AppL Meteorol . 35 , 1835 – 1845 .

Kim , J. and Mahrt , L . 1992 . Simple formulation of turbulent mixing in the stable free atmosphere and nocturnal boundary layer . Tellus 44A , 381 – 394 .

Kim , Y. , Masahito , U. , Nakagawa , F. , Tsunogai , U. , Harazono , Y. and co-authors . 2007 . Assessment of winter fluxes of CO2 and CH4 in boreal forest soils of central Alaska estimated by the profile method and the chamber method: a diagnosis of methane emission and implications for the regional carbon budget Tellus 59B , 223 - 233 .

Kowalski , A. S. and Serrano-Ortiz , P . 2007 . On the relationship between the eddy covariance, the turbulent flux, and surface exchange for a trace gas such as CO2 . Bound.-Layer Meteorol . 124 , 129 – 141 .

Lee , X . 1998 . On micrometeorological observations of surface-air ex-change over tall vegetation . Agri. Forest Meteorol . 91 , 39 – 49 .

Mahrt , L . 1986 . On the shallow motion approximations. J. Atmos. Sci . 43 , 1036 – 1044 .

Mammarella , I. , Kolari , P. , Rinne , J. , Keronen , P. and Pumpanen , J . 2007 . Determining the contribution of vertical advection to the net ecosystem exchange at Hyyti5.15. forest, Finland . Tellus 59B , 900 – 909 .

Massman , W. J. and Lee , X . 2002 . Eddy covariance flux corrections and uncertainties in long term studies of carbon and energy exchanges . Agri. Forest Meteorol . 113 , 121 – 144 .

Moraes , O. L. L. , Acevedo , O. C. , da Silva , R. , Magnago , R. and Siqueira , A. C . 2004 . Nocturnal surface-layer characteristics at the bottom of a valley . Bound.-Layer Meteorol . 112 , 159 – 177 .

NOAA, NASA and USAF. 1976. U.S. Standard Atmosphere , 1976 . U.S. Government Printing Office , Washington, DC .

Nobel , P. S . 2005 . Physicochemical and Environmental Plant Physiol-ogy . Elsevier Academic Press , Amsterdam .

Obulchov , A. M . 1971 . Turbulence in an atmosphere with a non-uniform temperature . Bound.-Layer Meteorol . 2 , 7 – 29 .

Oke , T. R . 1990 . Boundary Layer Climates . University Press , Cam-bridge .

Petty , G. W ., 2008. A First Course in Atmospheric Thermodynamics , Sundog, Madison.

Pihlatie , M. , Pumpanen , J. , Rinne , J. , Ilvesniemi , H. , Simojoki , A. and co-authors . 2007 . Gas concentration driven fluxes of nitrous oxide and carbon dioxide in boreal forest soil. Tellus 59B , 458 - 469 .

Pingintha , N. , Leclerc , M. Y. , Beasley , J. P. , Zhang , G. J. and Senthong , C . 2010 . Assessment of the soil CO2 gradient method for soil CO2 efflux measurements: comparison of six models in the calculation of the relative gas diffusion coefficient . Tellus 62B , 47 – 58 .

Rossby , C.-G . 1932 . Thermodynamics applied to air mass analysis . Meteorol. Papers 1 , 1 – 41 .

Seinfeld , J. H. and Pandis , S. N . 1998 . Atmospheric Chemistry and Physics: From Air Pollution to Climate Change , John Wiley & Sons, New York.

Sorensen Geernaert , L. L. , Geernaert , G. L. , Granby , K. and Asman , W. A. H . 1998 . Fluxes of soluble gases in the marine atmospheric surface layer . Tellus 50B , 111 – 127 .

Struthers , H. , Allan , W. , Lowe , D. C. and Bhaskaran , B . 2007 . A com-parison of the transport of long-lived atmospheric trace gas species from two advection schemes incorporated into an atmospheric general circulation model . Tellus 59B , 685 – 697 .

Stull , R. B . 1988 . An Introduction to Boundary Layer Meteorology . Kluwer , the Netherlands .

Sun , J. , Esbensen , S. K. and Mahrt , L . 1995 . Estimation of surface heat flux. J. Atmos. Sci . 52 , 3162 – 3171 .

Sutton , O. G . 1953 . Micrometeorology . McGraw-Hill Book Company , Inc ., New York .

UN Framework Convention on Climate Change 1997 . Kyoto Protocol to the United Nations Framework Convention on Climate Change , Kyoto , 23 .

Webb , E. K. , Pearman , G. I. and Leuning , R . 1980 . Correction of flux measurements for density effects due to heat and water vapour trans-fer . Q. J. R. Meteorol. Soc . 106 , 85 – 100 .

Wyngaard , J. C . 1984 . Towards convective boundary layer parameteri-zation: a scalar transport module. J. Atmos. Sci . 41 , 1959 – 1969 .

Wyngaard , J. C . 1990 . Scalar fluxes in the planetary boundary layer: theory, modeling, and measurement . Bound.-Layer Meteorol . 50 , 49 – 75 .

Wyngaard , J. C. and Brost , R. A . 1984 . Top-down and bottom-up diffu-sion of a scalar in the convective boundary layer. J. Atmos. Sci . 41 , 102 – 112 .

Wyngaard , J. C. and Cote , O. R . 1971 . The budgets of turbulent kinetic energy and temperature variance in the atmospheric surface layer. J. Atmos. Sci . 28 , 190 – 201 .

Wyngaard , J. C. , Siegel , A. and Wilczak , J. M . 1994 . On the response of a turbulent-pressure probe and the measurement of pressure transport . Bound.-Layer Meteorol . 69 , 379 – 396 .

Yi , C. , Davis , K. J. , Bakwin , P. S. , Berger , B. W. and Man , L. C . 2000 . Influence of advection on measurements of the net ecosystem-atmosphere exchange of CO2 from a very tall tower . J. Geophys. Res . 105 , 9991 – 9999 .

Zhang , J. , Lee , X. , Song , G. , and Han , S ., 2011 , Pressure correction to the long-term measurement of carbon dioxide flux , Agri. Forest Meteorol . 151 , 70 – 77 .

[CIT0001] Arya , S. P . 1988 . Introduction to Micrometeorology . Academic Press , San Diego .

[CIT0002] Baldocchi , D . 2008 . Breathing of the terrestrial biosphere: lessons learned from a global network of carbon dioxide flux measurement systems . Australian J. Bot . 56 , 1 – 26 .

[CIT0003] Baldocchi , D. D. , Hicks , B. B. and Meyers , T. P . 1988 . Measuring biosphere-atmosphere exchange of biologically-related gases with micrometeorological methods . Ecology 69 , 1331 – 1340 .

[CIT0004] Barenblatt , G.I . 2003 . Scaling . Cambridge University Press , Cambridge .

[CIT0005] Batchelor , G. K . 1967 . An Introduction to Fluid Dynamics . Cambridge University Press , Cambridge .

[CIT0006] Betts , A. K. and Albrecht , B. A . 1986 . Conserved variable analysis of the convective boundary layer thermodynamic structure over the tropical oceans. J. Atmos. Sci . 44 , 83 – 99 .

[CIT0007] Bird , R. B. , Stewart , W. E. and Lightfoot , E. N . 2002 . Transport Phe-nomena . John Wiley & Sons , Cambridge .

[CIT0008] Bres , M. and Hatzfeld , C . 1977 . Three-gas diffusion: experimental and theoretical study . Eur. J. PhysioL 371 , 227 – 233 .

[CIT0009] Buckingham , E . 1914 . On physically similar systems: illustrations of the use of dimensional equations . Phys. Rev . 4 , 345 – 376 .

[CIT0010] Businger , J. A . 1986 . Evaluation of the accuracy with which dry depo-sition can be measured with current micrometeorological techniques . J. Clim. AppL Meteorol . 25 , 1100 – 1124 .

[CIT0011] Businger , J. A. and Yaglom , A. M . 1971 . Introduction to Obulchov's paper on ‘Turbulence in an atmosphere with a non-uniform tempera-ture’ . Bound.-Layer MeteoroL 2 , 3 – 6 .

[CIT0012] Campbell , G. S. and Norman , J. M . 1998 . Environmental Biophysics . Springer-Verlag , New York .

[CIT0013] Davidson , E. A. and Trumbore , S. E . 1995 . Gas diffusivity and pro-duction of CO2 in the deep soils of the eastern Amazon . Tellus 47B , 550 – 565 .

[CIT0014] Fierer , N. , Chadwick , O. A. and Trumbore , S. E . 2005 . Production of CO2 in soil profiles of a California annual grassland . Ecosystems 8 , 412 – 429 .

[CIT0015] Finnigan , J. J . 2004 . A re-evaluation of long-term flux measurement techniques. Part II: Coordinate systems . Bound.-Layer MeteoroL 113 , 1 – 41 .

[CIT0016] Finnigan , J . 2008 . An introduction to flux measurements in difficult conditions . EcoL Appl . 18 , 1340 – 1350 .

[CIT0017] Finnigan , J. J . 2009 . Response to comment by Dr. A.S. Kowalski on “The storage term in eddy flux calculations” . Agri. Forest MeteoroL 149 , 725 – 729 .

[CIT0018] Finnigan , J. J. , Clement , R. , Malhi , Y. , Leuning , R. and Cleugh , H. A . 2003 . A re-evaluation of long-term flux measurement techniques. Part I: averaging and coordinate rotation . Bound.-Layer MeteoroL 107 , 1 – 48 .

[CIT0019] Foken , T . 2008 . Micrometeorology . Springer-Verlag , Berlin Heidelberg .

[CIT0020] Font , A. , Morgui , J.-A. , Curcoll , R. , Pouchet , I. , Caals , I. and co-authors . 2010 . Daily carbon surface fluxes in theWest Ebre (Ebro) watershed from aircraft profiling on late June 2007. Tellus 62B , 427 - 440 .

[CIT0021] Forster , P. , Ramaswamy , V , Artaxo , P. , Berntsen , N. L. , Betts , R. and co-authors . 2007 . Changes in atmospheric constituents and in radia-tive forcing. In: Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change eds. Solomon, S. , D. Qin , M. Manning , Z. Chen , M. Marquis et al.). Cambridge University Press , Cambridge, United Kingdom and New York, NY, USA .

[CIT0022] van Gorsel , E. , Leuning , R. , Cleugh , H. A. , Keith , H. and Suni , T . 2007 . Nocturnal carbon efflux: reconciliation of eddy covariance and cham-ber measurements using an alternative to the u*-threshold filtering technique . Tellus 59B , 397 – 403 .

[CIT0023] Ha , K.-J. and Mahrt , L . 2003 . Radiative and turbulent fluxes in the nocturnal boundary layer . Tellus 55A , 317 – 327 .

[CIT0024] Holton , J. R . 1992 . An Introduction to Dynamic Meteorology . Academic Press , San Diego .

[CIT0025] Kaimal , J. C. and Finnigan , J. J . 1994 . Atmospheric Boundary Layer Flows Their Measurement and Structure . Oxford University Press , New York .

[CIT0026] Katul , G. G. , Finkelstein , P. L. , Clarke , J. E and Ellestad , T. G . 1996 . An investigation of the conditional sampling method used to estimate fluxes of active, reactive, and passive scalars . J. AppL Meteorol . 35 , 1835 – 1845 .

[CIT0027] Kim , J. and Mahrt , L . 1992 . Simple formulation of turbulent mixing in the stable free atmosphere and nocturnal boundary layer . Tellus 44A , 381 – 394 .

[CIT0028] Kim , Y. , Masahito , U. , Nakagawa , F. , Tsunogai , U. , Harazono , Y. and co-authors . 2007 . Assessment of winter fluxes of CO2 and CH4 in boreal forest soils of central Alaska estimated by the profile method and the chamber method: a diagnosis of methane emission and implications for the regional carbon budget Tellus 59B , 223 - 233 .

[CIT0029] Kowalski , A. S. and Serrano-Ortiz , P . 2007 . On the relationship between the eddy covariance, the turbulent flux, and surface exchange for a trace gas such as CO2 . Bound.-Layer Meteorol . 124 , 129 – 141 .

[CIT0030] Lee , X . 1998 . On micrometeorological observations of surface-air ex-change over tall vegetation . Agri. Forest Meteorol . 91 , 39 – 49 .

[CIT0031] Mahrt , L . 1986 . On the shallow motion approximations. J. Atmos. Sci . 43 , 1036 – 1044 .

[CIT0032] Mammarella , I. , Kolari , P. , Rinne , J. , Keronen , P. and Pumpanen , J . 2007 . Determining the contribution of vertical advection to the net ecosystem exchange at Hyyti5.15. forest, Finland . Tellus 59B , 900 – 909 .

[CIT0033] Massman , W. J. and Lee , X . 2002 . Eddy covariance flux corrections and uncertainties in long term studies of carbon and energy exchanges . Agri. Forest Meteorol . 113 , 121 – 144 .

[CIT0034] Moraes , O. L. L. , Acevedo , O. C. , da Silva , R. , Magnago , R. and Siqueira , A. C . 2004 . Nocturnal surface-layer characteristics at the bottom of a valley . Bound.-Layer Meteorol . 112 , 159 – 177 .

[CIT0035] NOAA, NASA and USAF. 1976. U.S. Standard Atmosphere , 1976 . U.S. Government Printing Office , Washington, DC .

[CIT0036] Nobel , P. S . 2005 . Physicochemical and Environmental Plant Physiol-ogy . Elsevier Academic Press , Amsterdam .

[CIT0037] Obulchov , A. M . 1971 . Turbulence in an atmosphere with a non-uniform temperature . Bound.-Layer Meteorol . 2 , 7 – 29 .

[CIT0038] Oke , T. R . 1990 . Boundary Layer Climates . University Press , Cam-bridge .

[CIT0039] Petty , G. W ., 2008. A First Course in Atmospheric Thermodynamics , Sundog, Madison.

[CIT0040] Pihlatie , M. , Pumpanen , J. , Rinne , J. , Ilvesniemi , H. , Simojoki , A. and co-authors . 2007 . Gas concentration driven fluxes of nitrous oxide and carbon dioxide in boreal forest soil. Tellus 59B , 458 - 469 .

[CIT0041] Pingintha , N. , Leclerc , M. Y. , Beasley , J. P. , Zhang , G. J. and Senthong , C . 2010 . Assessment of the soil CO2 gradient method for soil CO2 efflux measurements: comparison of six models in the calculation of the relative gas diffusion coefficient . Tellus 62B , 47 – 58 .

[CIT0042] Rossby , C.-G . 1932 . Thermodynamics applied to air mass analysis . Meteorol. Papers 1 , 1 – 41 .

[CIT0043] Seinfeld , J. H. and Pandis , S. N . 1998 . Atmospheric Chemistry and Physics: From Air Pollution to Climate Change , John Wiley & Sons, New York.

[CIT0044] Sorensen Geernaert , L. L. , Geernaert , G. L. , Granby , K. and Asman , W. A. H . 1998 . Fluxes of soluble gases in the marine atmospheric surface layer . Tellus 50B , 111 – 127 .

[CIT0045] Struthers , H. , Allan , W. , Lowe , D. C. and Bhaskaran , B . 2007 . A com-parison of the transport of long-lived atmospheric trace gas species from two advection schemes incorporated into an atmospheric general circulation model . Tellus 59B , 685 – 697 .

[CIT0046] Stull , R. B . 1988 . An Introduction to Boundary Layer Meteorology . Kluwer , the Netherlands .

[CIT0047] Sun , J. , Esbensen , S. K. and Mahrt , L . 1995 . Estimation of surface heat flux. J. Atmos. Sci . 52 , 3162 – 3171 .

[CIT0048] Sutton , O. G . 1953 . Micrometeorology . McGraw-Hill Book Company , Inc ., New York .

[CIT0049] UN Framework Convention on Climate Change 1997 . Kyoto Protocol to the United Nations Framework Convention on Climate Change , Kyoto , 23 .

[CIT0050] Webb , E. K. , Pearman , G. I. and Leuning , R . 1980 . Correction of flux measurements for density effects due to heat and water vapour trans-fer . Q. J. R. Meteorol. Soc . 106 , 85 – 100 .

[CIT0051] Wyngaard , J. C . 1984 . Towards convective boundary layer parameteri-zation: a scalar transport module. J. Atmos. Sci . 41 , 1959 – 1969 .

[CIT0052] Wyngaard , J. C . 1990 . Scalar fluxes in the planetary boundary layer: theory, modeling, and measurement . Bound.-Layer Meteorol . 50 , 49 – 75 .

[CIT0053] Wyngaard , J. C. and Brost , R. A . 1984 . Top-down and bottom-up diffu-sion of a scalar in the convective boundary layer. J. Atmos. Sci . 41 , 102 – 112 .

[CIT0054] Wyngaard , J. C. and Cote , O. R . 1971 . The budgets of turbulent kinetic energy and temperature variance in the atmospheric surface layer. J. Atmos. Sci . 28 , 190 – 201 .

[CIT0055] Wyngaard , J. C. , Siegel , A. and Wilczak , J. M . 1994 . On the response of a turbulent-pressure probe and the measurement of pressure transport . Bound.-Layer Meteorol . 69 , 379 – 396 .

[CIT0056] Yi , C. , Davis , K. J. , Bakwin , P. S. , Berger , B. W. and Man , L. C . 2000 . Influence of advection on measurements of the net ecosystem-atmosphere exchange of CO2 from a very tall tower . J. Geophys. Res . 105 , 9991 – 9999 .

[CIT0057] Zhang , J. , Lee , X. , Song , G. , and Han , S ., 2011 , Pressure correction to the long-term measurement of carbon dioxide flux , Agri. Forest Meteorol . 151 , 70 – 77 .

Reading: Scalar arguments of the mathematical functions defining molecular and turbulent transport of...

Original Research Papers

Scalar arguments of the mathematical functions defining molecular and turbulent transport of heat and mass in compressible fluids

Authors:

Andrew S. Kowalski ,

Departamento de Física Aplicada, Facultad de Ciencias, Universidad de Granada; Centro Andaluz de Medio Ambiente (CEAMA), ES

X close

Daniel Argüeso

Departamento de Física Aplicada, Facultad de Ciencias, Universidad de Granada, ES

X close

Abstract

References