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Better Physics in Embedded Models: Iceberg arcing and Lake-surface profiles Aitbala Sargent, James L Fastook, Ted Scambos. University of Maine We thank the NSF, which has supported the development of this model over many years through several different grants. Aitbala Sargent, James L Fastook, Ted Scambos. University of Maine We thank the NSF, which has supported the development of this model over many years through several different grants. Slide 2 EMBEDDED MODELS Better physics, limited domain runs inside Low-resolution, larger domain model. Modeling the whole ice sheet allows margins to be internally generated. No need to specify flux or ice thickness along a boundary transecting an ice sheet. Specification of appropriate Boundary Conditions for limited-domain model, based on spatial and temporal interpolations of larger-domain model. Better physics, limited domain runs inside Low-resolution, larger domain model. Modeling the whole ice sheet allows margins to be internally generated. No need to specify flux or ice thickness along a boundary transecting an ice sheet. Specification of appropriate Boundary Conditions for limited-domain model, based on spatial and temporal interpolations of larger-domain model. Slide 3 Force Balance longitudinal drag (compression from up/down glacier) direction of flow basal drag lateral drag driving stress Slide 4 Shallow Ice Approximation Only stress allowed is xz, the basal drag. Velocity profile integrated strain rate. Quasi-2D, with Z integrated out. 1 degree of freedom per node (3D temperatures). Good for interior ice sheet and where longitudinal stresses can be neglected. Probably not very good for ice streams. basal drag driving stress direction of flow Slide 5 Barely Grounded Ice Shelf A modification of the Morland Equations for an ice shelf (MacAyeal and Hulbe). Quasi-2D model (X and Y, with Z integrated out). 3 degrees of freedom: (Ux, Uy, and h) vs 1 (h). Addition of friction term violates assumptions of the Morland derivation. Requires specification as to where ice stream occurs. direction of flow driving stress lateral drag longitudinal drag (compression from up/down glacier) Slide 6 Full Momentum Equation No stresses are neglected. True 3-D model. Computationally intensive, with 3-D representation of the ice sheet, X and Y nodes as well as layers in the Z dimension. 3 degrees of freedom per node (Ux, Uy, and Uz) as well as thickness in X and Y. (all three of these require 3-D temperature solutions). direction of flow basal drag lateral drag driving stress longitudinal drag (compression from up/down glacier) Slide 7 Field Equations Conservation of momentum, Conservation of mass, Conservation of energy, and Constitutive relation. Conservation of momentum, Conservation of mass, Conservation of energy, and Constitutive relation. Slide 8 The Full Momentum Equation Conservation of Momentum: Balance of Forces Flow Law, relating stress and strain rates. Effective viscosity, a function of the strain invariant. Strain rates and velocity gradients. Conservation of Momentum: Balance of Forces Flow Law, relating stress and strain rates. Effective viscosity, a function of the strain invariant. Strain rates and velocity gradients. Slide 9 The Heat Flow Equation The strain-heating term, a product of stress and strain rates. Time-dependent Conservation of energy. The total derivative as partial and advection term. The strain-heating term, a product of stress and strain rates. Time-dependent Conservation of energy. The total derivative as partial and advection term. Slide 10 The Continuity Equation Conservation of mass, time-rate of change of thickness, gradient of flux, and local mass balance. Slide 11 Work in Progress Sliding Boundary Conditions: flat bed: non-flat bed: Grid Resolution: largest grid solved: 25x25x10=6,250 points 6,250x4 (u,p)=25,000 variables 25,000x81(bandwidth)=2,025,000 matrix size Slide 12 2-D Applications Iceberg Edge Warping: Toe-up and Toe-down Configurations. Lake Vostok Trench and Trough Slide 13 Iceberg Edge Warping Past models: toe-down profiles Neils Reeh, 1968 theoretical model James Fastook, 1984 numerical model Text Slide 14 Iceberg Ponds, prelude to breakup Slide 15 Berg Profiles Slide 16 Berg Concepts Slide 17 Simulation Results Slide 18 Lake Vostok Radarsat image of the ice-sheet surface across subglacial Lake Vostok ( RADARSAT) Lake Vostok location map and survey area Slide 19 Image: M. Studinger Slide 20 East-West Transect: Surface and Bed Elevation Slide 21 Surface Evolution Slide 22 Slide 23 Velocity Evolution Slide 24 Slide 25 Velocities Magnitude Slide 26 X and Y Velocities Slide 27 Longitudinal Stresses and Strains Slide 28 Vertical Stresses and Strains Slide 29 Shear Stresses and Strains Slide 30 Strain Invariant Slide 31 3D Applications: A beginning Slide 32 3D Application: A beginning Slide 33 Slide 34 Slide 35 Slide 36 Slide 37 Slide 38 Slide 39 Slide 40 Slide 41 3D Application: Vertical Transect Slide 42 Slide 43 Slide 44 Slide 45 Slide 46 Slide 47 Slide 48 Slide 49 Slide 50 THANK YOU