DEVELOPMENT OF A COMPUTER SIMULATION SCHEME FOR TWO AND THREE DIMENSIONAL ICE SHEET DYNAMICS MODELS

• Main Authors: カワイ, シンイチ, ナカワ, マサヨシ, KAWAI, Shinichi, NAKAWO, Masayoshi
• Language: English
• Published: National Institute of Polar Research 1994
• Subjects: Ice Sheet; Polar meteorology and glaciology; Proceedings of the NIPR Symposium on Polar Meteorology and Glaciology
• Online Access: https://nipr.repo.nii.ac.jp/record/3865/files/KJ00000767973.pdf; https://doi.org/10.15094/00003865; https://nipr.repo.nii.ac.jp/records/3865

P(論文) We have developed a scheme for two and three dimensional ice sheet dynamics with the model considered by Mahaffy, assuming the basal sliding velocity to be zero. Mahaffy's model is given by ∂h/∂t=b-▽・q and q=-ck▽h, or c▽・(-k▽h)=b-∂h/∂t, where c={(2A)/(n+2)} (ρg)^n and k (x, y, t)=(▽h・▽h)^<(n-1)/2> (h-z_0)^<n+2>. We can lead the dimensionless form, in which c=1. In the two dimensional model, let Ω_1=[-x_1,x_1] which is the land area, and Ω_2=[-x_2,-x_1) ∪ (x_1,x_2], which is the sea area, where 0<x_1<x_2. We assume that q in Ω_2 is m times larger than in Ω_1 and that the initial shape of h is symmetric about x=0. Let 0≤x≤n△x, q_ =q((i-1/2) △x, k△t) (i=0,1,., n+1) and h_ =h (i△x, k△t)(i=0,1,., n), z_<0i>=z_0 (i△x) (i=0,1,., n). Then q_ and h_ are placed alternately. The finite difference representations of Mahaffy's model are q_ =-{(h_ -h_ )/△x}^n{(h_ +h_ )/2+(z_ +z_ ^-_1)/2}^<n+2> and h_ =h_ +△t{b-(q_ -q_ )/△x}. If i△x ⋴ Ω_2,mq_ is used instead of q_ . Boundary conditions are q_<0,k>=(-1)^n q_<1,k> and h_<n, k>=0. In the three dimensional model, let Ω be the region of interest and ∂Ω be the boundary of Ω. For both sides of Mahaffy's model, we multiply the weighting function W_l and integrate in the interior region Ω and apply Green's theorem, ⎰_Ω k▽h・▽W_ldΩ-⎰_<∂Ω>k (∂h/∂n) W_ldГ=⎰_Ω(b-∂h/∂t) W_ldΩ, where ∂h/∂n=▽h・n in which n is the outer normal vector of ∂Ω. We divided the region Ω into N small regions Ω^e. Let M be the number of nodes and assign a number from 1 to M to each node. Let h^^^^ be the approximation of h. [numerical formula] where N_m (x, y) are basis functions which are 1 at the node m and 0 in small regions which do not include the node m. We take N_1 as the weighting function. Let k=k(h), b=b(h), K_<l, m> (h)=⎰_Ω k{(∂N_m/∂x)(∂N_l/∂x)+(∂N_m/∂y)(∂N_l/∂y)}dΩ-⎰_<∂Ω>k(∂N_m/∂n) N_ldГ, C_<l, m>=⎰_ΩN_mN_ldΩ, ƒ_l(h)=⎰_ΩbN_ldΩ, K=(K_<l, m>)_<l, m=1,., M, > C=(C_<l, m>)_<l, m=1,., M> and f=(ƒ_<1,., ...