A Coordinate System Having Some Special Advantages for Numerical Forecasting

Abstract. Few ice sheet flow models have been developed that solve the complete set of mechanical equations. Until now, these models were limited to isotropic conditions. We present here a two-dimensional, finite difference method capable of solving the equations for the steady flow of a viscous, incompressible, anisotropic fluid with a free surface under isothermal conditions. It is not a standard method, especially with respect to the time discretization of the numerical scheme, and converges for very low Reynolds numbers. This method is applied here to the planar flow of anisotropic ice over fiat or irregular bedrock, with no-slip boundary conditions at the ice-bedrock interface. The results are presented here for Newtonian behavior in the vicinity of an ice divide. The ice is assumed to be isotropic at the ice sheet surface, with continuous and prescribed development of anisotropy with increasing depth. Going from isotropic to anisotropic situations, our results indicate that the free surface becomes flatter and the shear strain rates larger and more concentrated near the bedrock. The flow is less sensitive to variations of the bedrock topography in the anisotropic case than in the isotropic case. Furthermore, a new phenomenon appears in the anisotropic case: the partial stagnation of ice in the holes of the bedrock. These effects have significant consequences when dating the ice. The isochrones obtained in the anisotropic case are flatter and the anisotropic ice is more than 10% younger above the bumps and more than 100% older within the holes than for the isotropic ice.

Section: Free Surfacementioning

confidence: 99%

A numerical study of anisotropic, low Reynolds number, free surface flow for ice sheet modeling

Mangeney¹,

Califano²,

Hutter³

1997

“…This paper deals with the pressure gradient error in terrain following sigma coordinate models. Phillips [1957] introduced sigma coordinates into numerical weather prediction models many years ago. In oceanography, sigma coordinate models are typified by the widely used Princeton Ocean Model (POM) [Bluntberg and Mellor, 1987] and the Spectral Primitive Equation Model (SPEM) [Haidvogel et al, 1991].…”

Section: Introductionmentioning

confidence: 99%

On the pressure gradient error in sigma coordinate ocean models: A comparison with a laboratory experiment

Kliem¹,

Pietrzak²

1999

Abstract. Boundary-fitted vertical coordinates are frequently used in three-dimensional primitive equation models. The sigma coordinate transformation, in which the water column is divided into a number of layers independently of the water depth, is commonly used. Unfortunately, it is well known that this transformation can produce an error in the calculation of the pressure gradient terms. The error can be significant in regions with steep topography and large density gradients. The importance of this error in simulations of coastal currents is difficult to test in reality. The competing effects of the models dynamics, its sensitivity, for example, to the chosen grid resolution or numerical techniques, are hard to separate. In the following we first identify the pressure gradient error and assess its magnitude in relation to two analytical reference solutions. A number of commonly used techniques to reduce the error are compared. Of these techniques, z-level based pressure gradient calculations are shown to improve the simulation results. We then take a step in the direction of a more realistic simulation and use a laboratory experiment as our reference solution. The results demonstrate that a sigma coordinate model can be used in a region such as the Skagerrak where steep topography and large density gradients are present. Errors do exist which need to be taken into account when interpreting the model results. This is important, as the Skagerrak dominates the North Sea and Baltic Sea system, and models that run with a coarse grid resolution may lead to artificial flows.

“…However, more recent geological evidence [e.g., Williams, 1975] indicates that many parts of tropical continents were more arid during the late Pleistocene, in apparent contrast to the earlier notion of pluvial tropics during glacial periods. This paper describes the aridity (or lack of aridity) of the tropical climate of the model, evaluates the two contradictory viewpoints in the light of results from the numerical experiments, and proceeds to discuss how the lower using the sigma coordinate system in which pressure normalized by surface pressure is the vertical coordinate [Phillips, 1957]. The effects of subgrid scale mixing are represented by the nonlinear viscosity formulated by Smagorinsky [1963].…”

Section: Introductionmentioning

confidence: 99%

Simulation of the tropical climate of an ice age

Manabe¹,

Hahn²

1977

290

Numerical time integrations of a general circulation model of the atmosphere are performed with both modern and ice age boundary conditions. It is shown that the climate of continental portions of the tropics in the ice age simulation is much drier than that of the modern climate simulation. According to comparisons of results from the two experiments, tropical continental aridity of the ice age results from stronger surface outflow from (or weaker surface inflow into) continents. The intensification of outflow from (or weakening of inflow into) tropical continental regions results from the fact that in response to ice age boundary conditions, atmospheric temperature is reduced more over continents than over oceans. With the exception of high latitudes, boundary condition differences between the two experiments consist mainly of changes of the prescribed values of sea surface temperature and continental albedo. In order to evaluate the relative contributions of these changes in producing continental tropical aridity in the ice age simulation, a third numerical experiment is time-integrated in which a hybrid combination of ice age sea surface temperatures and modern continental albedo values is prescribed. From intercomparisons between results from this and the previous two experiments it is shown that the effect of increased continental albedo is mainly responsible for the weak Asian monsoon in the ice age simulation.