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At least 379 records · Page 21

Optimal measurement of ice-sheet deformation from surface-marker arrays

Surface strain rate is best observed by fitting a strain-rate ellipsoid to the measured movement of a stake network or other collection of surface features, using a least squares procedure. Error of the resulting fit varies as 1/(L delta t square root of N), where L is the stake separation, delta is the time period between initial and final stake survey, and n is the number of stakes in the network. This relation suggests that if n is sufficiently high, the traditional practice of revisiting stake-network sites on successive field seasons may be replaced by a less costly single year operation. A demonstration using Ross Ice Shelf data shows that reasonably accurate measurements are obtained from 12 stakes after only 4 days of deformation. It is possible for the least squares procedure to aid airborne photogrammetric surveys because reducing the time interval between survey and re-survey permits better surface feature recognition.

Macayeal, D. R.↗

Optimal measurement of ice-sheet deformation from surface-marker arrays

Surface strain rate is best observed by fitting a strain-rate ellipsoid to the measured movement of a stake network or other collection of surface features, using a least squares procedure. Error of the resulting fit varies as 1/(L delta t square root of N), where L is the stake separation, delta is the time period between initial and final stake survey, and n is the number of stakes in the network. This relation suggests that if n is sufficiently high, the traditional practice of revisiting stake-network sites on successive field seasons may be replaced by a less costly single year operation. A demonstration using Ross Ice Shelf data shows that reasonably accurate measurements are obtained from 12 stakes after only 4 days of deformation. It is possible for the least squares procedure to aid airborne photogrammetric surveys because reducing the time interval between survey and re-survey permits better surface feature recognition.

Macayeal, D. R.↗

Analysis of Antarctic Ice-Sheet Mass Balance from ICESat Measurements

If protoplanets formed from 10 to 20 kilometer diameter planetesimals in a runaway accretion process prior to their oligarchic growth into the terrestrial planets, it is only logical to ask where these planetesimals may have formed in order to assess the initial composition of the Earth. We have used Weidenschilling's model for the formation of comets (1997) to calculate an efficiency factor for the formation of planetesimals from the solar nebula, then used this factor to calculate the feeding zones that contribute to material contained within 10, 15 and 20 kilometer diameter planetesimals at 1 A.V. as a function of nebular mass. We find that for all reasonable nebular masses, these planetesimals contain a minimum of 3% water as ice by mass. The fraction of ice increases as the planetesimals increase in size and as the nebular mass decreases, since both factors increase the feeding zones from which solids in the final planetesimals are drawn. Is there really a problem with the current accretion scenario that makes the Earth too dry, or is it possible that the nascent Earth lost significant quantities of water in the final stages of accretion?

Zwally, H. Jay↗

A novel transformation of the ice sheet Stokes equations and some of its properties and applications

We introduce a novel transformation of the Stokes equations into a form closely resembling the shallow Blatter–Pattyn equations. The two forms differ by only a few additional terms, while their variational formulations differ only by a single term in each horizontal direction. Specifically, the variational formulation of the Blatter–Pattyn model drops the vertical velocity in the second invariant of the strain rate tensor. Here we make use of the new transformation in two ways. First, we consider incorporating the transformed equations into a code that can be very easily converted from a Stokes to a Blatter–Pattyn model, and vice versa, by switching these terms on or off. This may be generalized so that the Stokes model is switched on adaptively only where the Blatter–Pattyn model loses accuracy. Second, the key role played by the vertical velocity in the Blatter–Pattyn approximation motivates new approximations. Two examples are presented. These require a mesh that enables the discrete continuity equation to be invertible for the vertical velocity in terms of the horizontal velocity components. Examples of such meshes, such as the first-order P1–E0 mesh and the second-order P2–E1 mesh, are given in both 2D and 3D. However, the transformed Stokes model has the same type of gravity forcing as the Blatter–Pattyn model, determined by the ice surface slope, thereby forgoing some of the mesh generality of the traditional formulation of the Stokes model.

58 GEOSCIENCES↗