干雪的密度—介电常数模型的比较与评价
|
摘要
探地雷达能够较为高效地得到积雪的厚度,其前提条件是需要得到积雪中的电磁波波速。通常积雪的密度(ρ)和其介电常数(ε)存在相关关系,因此积雪的电磁波波速可以由积雪的密度得到。但是表征积雪密度和介电常数关系的方程多种多样,并且这些模型方程很少给出不确定度,导致选择合适的方程变得相当困难。针对已给出和未给出不确定度的模型方程进行比较,并以实测的实验数据为基础,选择最为合理的密度(ρ)-介电常数(ε)关系模型。
Ground Penetrating Radar( GPR) surveys on snow enable a rapid evaluation of snow thickness but necessitate a measurement of the wave velocity in the snowpack. Such quantity is often evaluated from density measurements,using the relationships connecting snow permittivity and density present in literature. Unfortunately such equations provide different results and are rarely reported with an associated uncertainty,making the choice between different models pretty difficult. In the present work we compare all the equations with uncertainties( when reported),suggesting which model can be considered as the most reliable. Such choice has also been corroborated by the analysis of experimental data.
Ground Penetrating Radar( GPR) surveys on snow enable a rapid evaluation of snow thickness but necessitate a measurement of the wave velocity in the snowpack. Such quantity is often evaluated from density measurements,using the relationships connecting snow permittivity and density present in literature. Unfortunately such equations provide different results and are rarely reported with an associated uncertainty,making the choice between different models pretty difficult. In the present work we compare all the equations with uncertainties( when reported),suggesting which model can be considered as the most reliable. Such choice has also been corroborated by the analysis of experimental data.
引文
[1] Godio,A. Georadar Measurements for the Snow CoverDensity[J]. American Journal of Applied Sciences,2009,6(3):414.
[2] Kinar,N. J.,J. W. Pomeroy. SAS2:the System forAcoustic Sensing of Snow[J]. Hydrological Processes,2015,29(18):4032-4050.
[3] Godio,A.,R. B. Rege. Analysis of Georadar Data toEstimate the Snow Depth Distribution[J]. Journal ofApplied Geophysics,2016(129):92-100.
[4] Bradford,John H.,Joel T. Harper,etal. Complex Die-lectric Permittivity Measurements from Ground-Pene-trating Radar Data to Estimate Snow Liquid Water Con-tent in the Pendular Regime[J]. Water Resources Re-search,2009,45(8):2263-2289.
[5] Holbrook,W. Steven,Scott N. Miller,etal. EstimatingSnow Water Equivalent over Long Mountain TransectsUsing Anowmobile-Mounted Ground-Penetrating Ra-dar[J]. Geophysics,2016,81(1):183-193.
[6] Godio,A.,R. B. Rege. The Mechanical Properties ofSnow and Ice of an Alpine Glacier Inferred by Integra-ting Seismic and GPR Methods[J]. Journal of AppliedGeophysics,2015(115):92-99.
[7] Forte,E.,et al. Velocity Analysis from Common OffsetGPR Data Inversion:Theory and Application to Syn-thetic and Real Data[J]. Geophysical Journal Interna-tional,2014,197(3):1471-1483.
[8] Previati,M.,A. Godio,etal. Validation of Spatial Var-iability of Snowpack Thickness and Density Obtainedwith GPR and TDR Methods[J]. Journal of AppliedGeophysics,2011,75(2):284-293.
[9] Di Paolo,F.,et al. Combined GPR and TDR Measure-ments for Snow Thickness and Density Estimation[C]//. Advanced Ground Penetrating Radar(IWAG-PR),2015 8th International Workshop on. IEEE,2015.
[10] Pfaffhuber,Andreas A.,Jan L. Lieser,etal. SnowThickness Profiling on Antarctic Sea Ice with GPR—Rapid and Accurate Measurements with the Potentialto Upscale Needles to a Haystack[J]. GeophysicalResearch Letters,2017,44(15):7836-7844.
[11] Forte,E.,et al. A New Fast Methodology to Estimatethe Density of Frozen Materials by Means of CommonOffset GPR Data[J]. Journal of Applied Geophysics,2013(99):135-145.
[12] Frolov,Anatoly D.,Yury Ya. Macheret. On Dielec-tric Properties of Dry and Wet Snow[J]. HydrologicalProcesses,1999,13(12‐13):1755-1760.
[13] Looyenga,H. Dielectric Constants of HeterogeneousMixtures[J]. Physica,1965,31(3):401-406.
[14] Chelidze,T. L.,A. I. Derevyanko,etal. ElectricalSpectroscopy of Heterogeneous Systems[M]. Kiev:Naukova Dumka,1977:231.
[15] BIPM,IEC,et al. Evaluation of Measurement Data—Guide to the Expression of Uncertainty in Measure-ment[C]//. Joint Committee for Guides in Metrology(JCGM 100:2008,GUM 1995 with minor correc-tions),2008.
[16] Robin,G. de Q.,S. Evans,etal. Interpretation ofRadio Echo Sounding in Polar Ice Sheets[J]. Phil.Trans. R. Soc. Lond.,1969,A 265(1166):437-505.
[17] Denoth,A. An Electronic Device for Long-TermSnow Wetness Recording[J]. Annals of Glaciology,1994(19):104-106.
[18] Kovacs,Austin,Anthony J. Gow,etal. A Reassess-ment of the In-Situ Dielectric Constant of Polar Firn[C]//. No. CRREL-93-26. COLD REGIONSRESEARCH AND ENGINEERING LAB HANOVERNH,1993.
[19] Kovacs,Austin,Anthony J. Gow,etal. The In-SituDielectric Constant of Polar Firn Revisited[J]. ColdRegions Science and Technology,1995,23(3):245-256.
[20] Matzler,Christian. MicrowavePermittivity of Dry Snow[J]. IEEE Transactions on Geoscience and RemoteSensing,1996,34(2):573-581.
[21] Denoth,A. Snow Dielectric Measurements[J]. Ad-vances in Space Research,1989,9(1):233-243.
[22] Achammer,T. H.,A. Denoth. Snow Dielectric Prop-erties:from DC to Microwave X-Band[J]. Annals ofGlaciology,1994(19):92-96.
[23] Kwok,Ron,G. F. Cunningham. ICESat over Arctic-Sea Ice:Estimation of Snow Depth and Ice Thickness[J]. Journal of Geophysical Research:Oceans,2008,113(C8).
[24] Robin,G. de Q. Velocity ofRadio Waves in Ice byMeans of a Bore-Hole Interferometric Technique[J]. Journal of Glaciology,1975,15(73):151-159.
[25] Kuroiwa,Daisuke. The Dielectric Property of Snow[M]. London:International Association of Hydrologi-cal Sciences Publication,1954.
[26] Glen,J. W.,J. G. Paren. The Electrical Propertiesof Snow and Ice[J]. Journal of Glaciology,1975,15(73):15-38.
[27] Ambach,W.,A. Denoth. Studies on the DielectricProperties of Snow[J]. Zeitschrift für Gletscherkundeund Glazialgeologie,1972(8):113-1223.
[28] Stiles,W. H.,F. T. Ulaby. Dielectric Properties ofSnow[M]. Kansas:The University of Kansas Centerfor Research,Remote Sensing Laboratory,RSL Tech-nical Report,1981.
[29] Hallikainen,M.,F. Ulaby,M. Abdel-Razik.Measurements of the Dielectric Properties of Snow inthe 4-18 GHz Frequency Range[C]//. MicrowaveConference,1982. 12th European. IEEE,1982.
[30] Denoth,A.,et al. A comparative Study of Instrumentsfor Measuring the Liquid Water Content of Snow[J].Journal of Applied Physics,1984,56(7):2154-2160.
[31] Tiuri,M.,et al. The Complex Dielectric Constant ofSnow at Microwave Frequencies[J]. IEEE Journal ofOceanic Engineering,1984,9(5):377-382.
[32] Stein,Jean,Gaetan Laberge,etal. Monitoring the DryDensity and the Liquid Water Content of Snow UsingTime Domain Reflectometry(TDR)[J]. Cold Re-gions Science and Technology,1997,25(2):123-136.
[33] Schneebeli,Martin,et al. Measurement of Density andWetness in Snow Using Time-Domain Reflectometry[J]. Annals of Glaciology,1998(26):69-72.
[34] Ball,James AR. Characteristic Impedance of Unbal-anced TDR Probes[J]. IEEE Transactions on Instru-mentation and Measurement,2002,51(3):532-536.
[35] Eisen,Olaf,et al. Alpine Ice Cores and Ground Pene-trating Radar:Combined Investigations for Glaciologi-cal and Climatic Interpretations of a Cold Alpine IceBody[J]. Tellus B:Chemical and Physical Meteorolo-gy,2011,55(5):1007-1017.
[2] Kinar,N. J.,J. W. Pomeroy. SAS2:the System forAcoustic Sensing of Snow[J]. Hydrological Processes,2015,29(18):4032-4050.
[3] Godio,A.,R. B. Rege. Analysis of Georadar Data toEstimate the Snow Depth Distribution[J]. Journal ofApplied Geophysics,2016(129):92-100.
[4] Bradford,John H.,Joel T. Harper,etal. Complex Die-lectric Permittivity Measurements from Ground-Pene-trating Radar Data to Estimate Snow Liquid Water Con-tent in the Pendular Regime[J]. Water Resources Re-search,2009,45(8):2263-2289.
[5] Holbrook,W. Steven,Scott N. Miller,etal. EstimatingSnow Water Equivalent over Long Mountain TransectsUsing Anowmobile-Mounted Ground-Penetrating Ra-dar[J]. Geophysics,2016,81(1):183-193.
[6] Godio,A.,R. B. Rege. The Mechanical Properties ofSnow and Ice of an Alpine Glacier Inferred by Integra-ting Seismic and GPR Methods[J]. Journal of AppliedGeophysics,2015(115):92-99.
[7] Forte,E.,et al. Velocity Analysis from Common OffsetGPR Data Inversion:Theory and Application to Syn-thetic and Real Data[J]. Geophysical Journal Interna-tional,2014,197(3):1471-1483.
[8] Previati,M.,A. Godio,etal. Validation of Spatial Var-iability of Snowpack Thickness and Density Obtainedwith GPR and TDR Methods[J]. Journal of AppliedGeophysics,2011,75(2):284-293.
[9] Di Paolo,F.,et al. Combined GPR and TDR Measure-ments for Snow Thickness and Density Estimation[C]//. Advanced Ground Penetrating Radar(IWAG-PR),2015 8th International Workshop on. IEEE,2015.
[10] Pfaffhuber,Andreas A.,Jan L. Lieser,etal. SnowThickness Profiling on Antarctic Sea Ice with GPR—Rapid and Accurate Measurements with the Potentialto Upscale Needles to a Haystack[J]. GeophysicalResearch Letters,2017,44(15):7836-7844.
[11] Forte,E.,et al. A New Fast Methodology to Estimatethe Density of Frozen Materials by Means of CommonOffset GPR Data[J]. Journal of Applied Geophysics,2013(99):135-145.
[12] Frolov,Anatoly D.,Yury Ya. Macheret. On Dielec-tric Properties of Dry and Wet Snow[J]. HydrologicalProcesses,1999,13(12‐13):1755-1760.
[13] Looyenga,H. Dielectric Constants of HeterogeneousMixtures[J]. Physica,1965,31(3):401-406.
[14] Chelidze,T. L.,A. I. Derevyanko,etal. ElectricalSpectroscopy of Heterogeneous Systems[M]. Kiev:Naukova Dumka,1977:231.
[15] BIPM,IEC,et al. Evaluation of Measurement Data—Guide to the Expression of Uncertainty in Measure-ment[C]//. Joint Committee for Guides in Metrology(JCGM 100:2008,GUM 1995 with minor correc-tions),2008.
[16] Robin,G. de Q.,S. Evans,etal. Interpretation ofRadio Echo Sounding in Polar Ice Sheets[J]. Phil.Trans. R. Soc. Lond.,1969,A 265(1166):437-505.
[17] Denoth,A. An Electronic Device for Long-TermSnow Wetness Recording[J]. Annals of Glaciology,1994(19):104-106.
[18] Kovacs,Austin,Anthony J. Gow,etal. A Reassess-ment of the In-Situ Dielectric Constant of Polar Firn[C]//. No. CRREL-93-26. COLD REGIONSRESEARCH AND ENGINEERING LAB HANOVERNH,1993.
[19] Kovacs,Austin,Anthony J. Gow,etal. The In-SituDielectric Constant of Polar Firn Revisited[J]. ColdRegions Science and Technology,1995,23(3):245-256.
[20] Matzler,Christian. MicrowavePermittivity of Dry Snow[J]. IEEE Transactions on Geoscience and RemoteSensing,1996,34(2):573-581.
[21] Denoth,A. Snow Dielectric Measurements[J]. Ad-vances in Space Research,1989,9(1):233-243.
[22] Achammer,T. H.,A. Denoth. Snow Dielectric Prop-erties:from DC to Microwave X-Band[J]. Annals ofGlaciology,1994(19):92-96.
[23] Kwok,Ron,G. F. Cunningham. ICESat over Arctic-Sea Ice:Estimation of Snow Depth and Ice Thickness[J]. Journal of Geophysical Research:Oceans,2008,113(C8).
[24] Robin,G. de Q. Velocity ofRadio Waves in Ice byMeans of a Bore-Hole Interferometric Technique[J]. Journal of Glaciology,1975,15(73):151-159.
[25] Kuroiwa,Daisuke. The Dielectric Property of Snow[M]. London:International Association of Hydrologi-cal Sciences Publication,1954.
[26] Glen,J. W.,J. G. Paren. The Electrical Propertiesof Snow and Ice[J]. Journal of Glaciology,1975,15(73):15-38.
[27] Ambach,W.,A. Denoth. Studies on the DielectricProperties of Snow[J]. Zeitschrift für Gletscherkundeund Glazialgeologie,1972(8):113-1223.
[28] Stiles,W. H.,F. T. Ulaby. Dielectric Properties ofSnow[M]. Kansas:The University of Kansas Centerfor Research,Remote Sensing Laboratory,RSL Tech-nical Report,1981.
[29] Hallikainen,M.,F. Ulaby,M. Abdel-Razik.Measurements of the Dielectric Properties of Snow inthe 4-18 GHz Frequency Range[C]//. MicrowaveConference,1982. 12th European. IEEE,1982.
[30] Denoth,A.,et al. A comparative Study of Instrumentsfor Measuring the Liquid Water Content of Snow[J].Journal of Applied Physics,1984,56(7):2154-2160.
[31] Tiuri,M.,et al. The Complex Dielectric Constant ofSnow at Microwave Frequencies[J]. IEEE Journal ofOceanic Engineering,1984,9(5):377-382.
[32] Stein,Jean,Gaetan Laberge,etal. Monitoring the DryDensity and the Liquid Water Content of Snow UsingTime Domain Reflectometry(TDR)[J]. Cold Re-gions Science and Technology,1997,25(2):123-136.
[33] Schneebeli,Martin,et al. Measurement of Density andWetness in Snow Using Time-Domain Reflectometry[J]. Annals of Glaciology,1998(26):69-72.
[34] Ball,James AR. Characteristic Impedance of Unbal-anced TDR Probes[J]. IEEE Transactions on Instru-mentation and Measurement,2002,51(3):532-536.
[35] Eisen,Olaf,et al. Alpine Ice Cores and Ground Pene-trating Radar:Combined Investigations for Glaciologi-cal and Climatic Interpretations of a Cold Alpine IceBody[J]. Tellus B:Chemical and Physical Meteorolo-gy,2011,55(5):1007-1017.