A theoretical steady state profile of ice sheets (two-dimentional model)

• Main Authors: 永田 武, Takesi Nagata
• Format: Report
• Language: English
• Published: 国立極地研究所 1977
• Subjects: 551.32; Greenland; Ice Sheet
• Online Access: https://nipr.repo.nii.ac.jp/?action=repository_uri&item_id=7961; http://id.nii.ac.jp/1291/00007961/; https://nipr.repo.nii.ac.jp/?action=repository_action_common_download&item_id=7961&item_no=1&attribute_id=18&file_no=1

氷床の断面形状に関するNyeの理論を,氷床内の氷質量保存の原則に基づいて改訂した. Nyeの氷床模型,さらにそれを改変したHaefeliの氷床模型の双方とも,質量保存則を満足せず,したがって両氷床模型とも定常状態を保ち得ないからである.新たに提案する理論においては,氷床中の氷質量保存法則を[numerical formula]で表し,NyeおよびHaefeliの仮定bx=uhとは異なる。ここに,cosθ・dis=dx, -dh/dx=tanθ, またbとh(x)はそれぞれ氷集積速度および氷床面の高さを表す。理論的計算の結果,定常氷床断面形状は[numerical formula]で与えられる(図2).ここに,x=0でh=H,またx=Lでh=0を以ってHおよびLを定義してある.この新定常氷床模型は,もちろん氷床内の氷質量保存の条件を満足するし,積水域と剥水域の境に当たる定常点を量的に定め得るほか,氷床内の氷流の流線分布(図3)を求めることができる.現在,もっとも詳しく測定されているグリーンランドの氷床断面と新定常氷床模型を比べた結果,両者の一致は十分満足できると結論できる(図4). The Nye's kinematic theory of ice sheet profiles is revised on the basis of the conservation law of ice mass, because the Nye's ice sheet model or the revised Haefeli's model does not satisfy the ice mass conservation law and therefore they cannot have a steady state. In the present revised theory, the mass conservation condition is represented by [numerical formula] in place of Nye-Haefeli assumption that bx=uh, where cos θ・ds=dx, -dh/dx=tanθ, and b and h(x) denote respectively the ice accumulation rate and the height of ice sheet surface. Then, the revised ice sheet profile is expressed by [numerical formula], where h=H at x=0 and x=L at h=0. This ice sheet profile model satisfies the ice mass conservation within the ice sheet. In this model, the equilibrium point to separate the ablation area from the accumulation area is clearly defined, and the stream-lines of ice now within the ice sheet are explicitly determined. It seems further that the agreement of the present steady state theoretical model of ice sheet profile with the observed data in Greenland is satisfactory.