ALBERT

Note: Contents List of contributors Introduction Part I Geophysical methods 1 Electrical methods / C. Kneisel and C. Hauck 1.1 Introduction 1.2 Measurement principles 1.3 Data acquisition 1.4 Data processing 1.5 Periglacial applications and particularities 1.6 Conclusions 1.7 Checklist References 2 Electromagnetic methods / A. Hardt and C. Hauck 2.1 Introduction 2.2 Background 2.3 Periglacial applications and particularities 2.4 Conclusions 2.5 Checklist References 3 Refraction seismics / L. Schrott and T. Hoffmann 3.1 Introduction 3.2 Measurement principles 3.3 Limitations of seismic refraction based on measurement principles 3.4 Data acquisition 3.5 Data processing 3.6 Periglacial applications and particularities 3.7 Checklist References 4 Ground-penetrating radar / I. Berthling and K. Melvold 4.1 Introduction 4.2 Measurement principles 4.3 Data acqusition 4.4 Data processing 4.5 Periglacial applications and particularities 4.6 Recommendations References Part Il Case studies 5 Typology of vertical electrical soundings for permafrost/ground ice investigation in the forefields of small alpine glaciers / R. Delaloye and C. Lambiel 5.1 Introduction 5.2 Method 5.3 Typology 5.4 Conclusions References 6 ERT imaging for frozen ground detection / M. Ishikawa 6.1 Introduction 6.2 Data acquisition and quality control 6.3 Case studies 6.4 Summary References 7 Electrical resistivity values of frozen soil from YES and TEM field observations and laboratory experiments / K. Harada 7.1 Introduction 7.2 Methods 7.3 Results 7.4 Summary References 8 Results of geophysical surveys on Kasprowy Wierch, the Tatra Mountains, Poland / W. Dobinski, B. Zogala, K. Wzietek and L. Litwin 8.1 Introduction 8.2 Field site 8.3 Methods 8.4 Measurements 8.5 Analysis and interpretation of the measurements 8.6 Conclusions References 9 Reassessment of DC resistivity in rock glaciers by comparing with P-wave velocity: a case study in the Swiss Alps / A. Ikeda 9.1 Introduction 9.2 Methods 9.3 Field sites with borehole information 9.4 Results 9.5 Discussion 9.6 Conclusions References 10 Quantifying the ice content in low-altitude scree slopes using geophysical methods / C. Hauck and C. Kneisel 10.1 Introduction 10.2 Methods 10.3 Field sites 10.4 Results 10.5 Discussion and conclusions References 11 The use of GPR in determining talus thickness and talus structure / O. Sass 11.1 Introduction 11.2 Study sites and data acquisition 11.3 Results 11.4 Conclusions References 12 GPR soundings of rock glaciers on Svalbard / I. Berthling, B. Etzelmüller, H. Farbrot, K. Isaksen, M. Wåle and R. Ødegård 12.1 Introduction 12.2 Methods 12.3 Results and interpretation 12.4 Discussion References 13 Arctic glaciers and ground-penetrating radar. Case study: Stagnation Glacier, Bylot Island, Canada / T. Irvine-Fynn and B. Moorman 13.1 Introduction 13.2 Field site 13.3 Field methods 13.4 Processing methods 13.5 Results 13.6 Discussion 13.7 Conclusions References 14 Mapping of subglacial topography using GPR for determining subglacial hydraulic conditions / K. Melvold and T. V. Schuler 14.1 Introduction 14.2 Field site 14.3 Methodology 14.4 Results 14.5 Discussion 14.6 Conclusions References 15 Snow measurements using GPR: example from Amundsenisen, Svalbard / K. Melvold 15.1 Introduction 15.2 GPR and GPS equipment and measurements 15:3 Data processing 15.4 Results and discussion 15.5 Conclusions References 16 Mapping frazil ice conditions in rivers using ground penetrating radar / I. Berthling, H. Benjaminsen and A. Kvambekk 16J Introduction 16.2 Setting and field procedures 16.3 Results 16.4 Discussion 16.5 Conclusions References Contents Appendix Tables of geophysical parameters for periglacial environments Index

Note: Contents Preface Part 1 Mathematical tools M 1 Algebra of vectors M 1.1 Basic concepts and definitions M 1.2 Reference frames M 1.3 Vector multiplication M 1.4 Reciprocal coordinate systems M 1.5 Vector representations M 1.6 Products of vectors in general coordinate systems M 1.7 Problems M 2 Vector functions M 2.1 Basic definitions and operations M 2.2 Special dyadics M 2.3 Principal-axis transformation of symmetric tensors M 2.4 Invariants of a dyadic M 2.5 Tensor algebra M 2.6 Problems M 3 Differential relations M 3.1 Differentiation of extensive functions M 3.2 The Hamilton operator in generalized coordinate systems M 3.3 The spatial derivative of the basis vectors M 3.4 Differential invariants in generalized coordinate systems M 3.5 Additional applications M 3.6 Problems M 4 Coordinate transformations M 4.1 Transformation relations of time-independent coordinate systems M 4.2 Transformation relations of time-dependent coordinate systems M 4.3 Problems M 5 The method of covariant differentiation M 5.1 Spatial differentiation of vectors and dyadics M 5.2 Time differentiation of vectors and dyadics M 5.3 The local dyadic of vP M 5.4 Problems M 6 Integral operations M 6.1 Curves, surfaces, and volumes in the general qi system M 6.2 Line integrals, surface integrals, and volume integrals M 6.3 Integral theorems M 6.4 Fluid lines, surfaces, and volumes M 6.5 Time differentiation of fluid integrals M 6.6 The general form of the budget equation M 6.7 Gauss' theorem and the Dirac delta function M 6.8 Solution of Poisson's differential equation M 6.9 Appendix: Remarks on Euclidian and Riemannian spaces M 6.10 Problems M 7 Introduction to the concepts of nonlinear dynamics M 7.1 One-dimensional flow M 7.2 Two-dimensional flow Part 2 Dynamics of the atmosphere 1 The laws of atmospheric motion 1.1 The equation of absolute motion 1.2 The energy budget in the absolute reference system 1.3 The geographical coordinate system 1.4 The equation of relative motion 1.5 The energy budget of the general relative system 1.6 The decomposition of the equation of motion 1.7 Problems 2 Scale analysis 2.1 An outline of the method 2.2 Practical formulation of the dimensionless flow numbers 2.3 Scale analysis of large-scale frictionless motion 2.4 The geostrophic wind and the Euier wind 2.5 The equation of motion on a tangential plane 2.6 Problems 3 The material and the local description of flow 3.1 The description of Lagrange 3.2 Lagrange's version of the continuity equation 3.3 An example of the use of Lagrangian coordinates 3.4 The local description of Euler 3.5 Transformation from the Eulerian to the Lagrangian system 3.6 Problems 4 Atmospheric flow fields 4.1 The velocity dyadic 4.2 The deformation of the continuum 4.3 Individual changes with time of geometric fluid configurations 4.4 Problems 5 The Navier-Stokes stress tensor 5.1 The general stress tensor 5.2 Equilibrium conditions in the stress field 5.3 Symmetry of the stress tensor 5.4 The frictional stress tensor and the deformation dyadic 5.5 Problems 6 The Helmholtz theorem 6.1 The three-dimensional Helmholtz theorem 6.2 The two-dimensional Helmholtz theorem 6.3 Problems 7 Kinematics of two-dimensional flow 7.1 Atmospheric flow fields 7.2 Two-dimensional streamlines and normals 7.3 Streamlines in a drifting coordinate system 7.4 Problems 8 Natural coordinates 8.1 Introduction 8.2 Differential definitions of the coordinate lines 8.3 Metric relationships 8.4 Blaton's equation 8.5 Individual and local time derivatives of the velocity 8.6 Differential invariants 8.7 The equation of motion for frictionless horizontal flow 8.8 The gradient wind relation 8.9 Problems 9 Boundary surfaces and boundary conditions 9.1 Introduction 9.2 Differential operations at discontinuity surfaces 9.3 Particle invariance at boundary surfaces, displacement velocities 9.4 The kinematic boundary-surface condition 9.5 The dynamic boundary-surface condition 9.6 The zeroth-order discontinuity surface 9.7 An example of a first-order discontinuity surface 9.8 Problems 10 Circulation and vorticity theorems 10.1 ErteFs form of the continuity equation 10.2 The baroclinic Weber transformation 10.3 The baroclinic Ertel-Rossby invariant 10.4 Circulation and vorticity theorems for frictionless baroclinic flow 10.5 Circulation and vorticity theorems for frictionless barotropic flow 10.6 Problems 11 Turbulent systems 11.1 Simple averages and fluctuations 11.2 Weighted averages and fluctuations 11.3 Averaging the individual time derivative and the budget operator 11.4 Integral means 11.5 Budget equations of the turbulent system 11.6 The energy budget of the turbulent system 11.7 Diagnostic and prognostic equations of turbulent systems 11.8 Production of entropy in the microturbulent system 11.9 Problems 12 An excursion into spectral turbulence theory 12.1 Fourier Representation of the continuity equation and the equation of motion 12.2 The budget equation for the amplitude of the kinetic energy 12.3 Isotropie conditions, the transition to the continuous wavenumber space 12.4 The Heisenberg spectrum 12.5 Relations for the Heisenberg exchange coefficient 12.6 A prognostic equation for the exchange coefficient 12.7 Concluding remarks on closure procedures 12.8 Problems 13 The atmospheric boundary layer 13.1 Introduction 13.2 Prandtl-layer theory 13.3 The Monin-Obukhov similarity theory of the neutral Prandtl layer 13.4 The Monin-Obukhov similarity theory of the diabatic Prandtl layer 13.5 Application of the Prandtl-layer theory in numerical prognostic models 13.6 The fluxes, the dissipation of energy, and the exchange coefficients 13.7 The interface condition at the earth's surface 13.8 The Ekman layer - the classical approach 13.9 The composite Ekman layer 13.10 Ekman pumping 13.11 Appendix A: Dimensional analysis 13.12 Appendix B: The mixing length 13.13 Problems 14 Wave motion in the atmosphere 14.1 The representation of waves 14.2 The group velocity 14.3 Perturbation theory 14.4 Pure sound waves 14.5 Sound waves and gravity waves 14.6 Lamb waves 14.7 Lee waves 14.8 Propagation of energy 14.9 External gravity waves 14.10 Internal gravity waves 14.11 Nonlinear waves in the atmosphere 14.12 Problems 15 The barotropic model 15.1 The basic assumptions of the barotropic model 15.2 The tinfiltered barotropic prediction model 15.3 The filtered barotropic model 15.4 Barotropic instability 15.5 The mechanism of barotropic development 15.6 Appendix 15.7 Problems 16 Rossby waves 16.1 One-and two-dimensional Rossby waves 16.2 Three-dimensional Rossby waves 16.3 Normal-mode considerations 16.4 Energy transport by Rossby waves 16.5 The influence of friction on the stationary Rossby wave 16.6 Barotropic equatorial waves 16.7 The principle of geostrophic adjustment 16.8 Appendix 16.9 Problems 17 Inertial and dynamic stability 17.1 Inertial motion in a horizontally homogeneous pressure field 17.2 Inertial motion in a homogeneous geostrophic wind field 17.3 Inertial motion in a geostrophic shear wind field 17.4 Derivation of the stability criteria in the geostrophic wind field 17.5 Sectorial stability and instability 17.6 Sectorial stability for normal atmospheric conditions 17.7 Sectorial stability and instability with permanent adaptation 17.8 Problems 18 The equation of motion in general coordinate systems 18.1 Introduction 18.2 The covariant equation of motion in general coordinate systems 18.3 The contravariant equation of motion in general 18.4 The equation of motion in orthogonal coordinate systems 18.5 Lagrange's equation of motion 18.6 Hamilton's equation of motion 18.7 Appendix 18.8 Problems 19 The geographical coordinate systems 19.1 The equation of motion 19.2 Application of Lagrange's equation of motion 19.3 The first metric simplification 19.4 The coordinate simplification 19.5 The continuity equation 19.6 Problems 20 The stereographic coordinate system 20.1 The stereographic projection 20.2 Metric forms in stereographic coordinates 20.

Note: Contents: Contributors. - Preface. - Introduction and Scientific Background / J.C.R. Hunt, J. Norbury and I. Roulstone. - 1. A view of the equations of meteorological dynamics and various approximations / A. A. White. - 2. Extended-geostrophic Euler-Poincare models for mesoscale oceanographic flow / J. S. Allen, D. D. Holm and P. A. Newberger. - 3. Fast singular oscillating limits of stably-stratified 3D Euler and Navier-Stokes equations and ageostrophic wave fronts / A. Babin, A. Mahalov and B. Nicolaenko. - 4. New mathematical developments in atmosphere and ocean dynamics, and their application to computer simulations / M. J. P. Cullen. - 5. Rearrangements of functions with applications to meteorology and ideal fluid flow / R. J. Douglas. - 6. Statistical methods in atmospheric dynamics: probability metrics and discrepancy measures as a means of defining balance / S. Baigent and J. Norbury.