WEKO3
アイテム
{"_buckets": {"deposit": "850fc702-1183-4e2c-81c2-f24aab60b741"}, "_deposit": {"created_by": 4, "id": "3865", "owners": [4], "pid": {"revision_id": 0, "type": "depid", "value": "3865"}, "status": "published"}, "_oai": {"id": "oai:nipr.repo.nii.ac.jp:00003865", "sets": ["532"]}, "author_link": ["6440", "6443", "6442", "6441"], "item_1_alternative_title_5": {"attribute_name": "論文名よみ", "attribute_value_mlt": [{"subitem_alternative_title": "DEVELOPMENT OF A COMPUTER SIMULATION SCHEME FOR TWO AND THREE DIMENSIONAL ICE SHEET DYNAMICS MODELS"}]}, "item_1_biblio_info_14": {"attribute_name": "書誌情報", "attribute_value_mlt": [{"bibliographicIssueDates": {"bibliographicIssueDate": "1994-11", "bibliographicIssueDateType": "Issued"}, "bibliographicPageStart": "208", "bibliographicVolumeNumber": "8", "bibliographic_titles": [{"bibliographic_title": "Proceedings of the NIPR Symposium on Polar Meteorology and Glaciology"}]}]}, "item_1_creator_7": {"attribute_name": "著者名よみ", "attribute_type": "creator", "attribute_value_mlt": [{"creatorNames": [{"creatorName": "カワイ, シンイチ"}], "nameIdentifiers": [{"nameIdentifier": "6440", "nameIdentifierScheme": "WEKO"}]}, {"creatorNames": [{"creatorName": "ナカワ, マサヨシ"}], "nameIdentifiers": [{"nameIdentifier": "6441", "nameIdentifierScheme": "WEKO"}]}]}, "item_1_creator_8": {"attribute_name": "著者名(英)", "attribute_type": "creator", "attribute_value_mlt": [{"creatorNames": [{"creatorName": "KAWAI, Shinichi", "creatorNameLang": "en"}], "nameIdentifiers": [{"nameIdentifier": "6442", "nameIdentifierScheme": "WEKO"}]}, {"creatorNames": [{"creatorName": "NAKAWO, Masayoshi", "creatorNameLang": "en"}], "nameIdentifiers": [{"nameIdentifier": "6443", "nameIdentifierScheme": "WEKO"}]}]}, "item_1_description_1": {"attribute_name": "ページ属性", "attribute_value_mlt": [{"subitem_description": "P(論文)", "subitem_description_type": "Other"}]}, "item_1_description_12": {"attribute_name": "抄録(英)", "attribute_value_mlt": [{"subitem_description": "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\u0027s model is given by ∂h/∂t=b-\u0026xdtri;・q and q=-ck\u0026xdtri;h, or c\u0026xdtri;・(-k\u0026xdtri;h)=b-∂h/∂t, where c={(2A)/(n+2)} (ρg)^n and k (x, y, t)=(\u0026xdtri;h・\u0026xdtri;h)^\u003c(n-1)/2\u003e (h-z_0)^\u003cn+2\u003e. 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\u003cx_1\u003cx_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\u0026le;x\u0026le;n\u0026xutri;x, q_\u003ci, k\u003e=q((i-1/2) \u0026xutri;x, k\u0026xutri;t) (i=0,1,..., n+1) and h_\u003ci, k\u003e=h (i\u0026xutri;x, k\u0026xutri;t)(i=0,1,..., n), z_\u003c0i\u003e=z_0 (i\u0026xutri;x) (i=0,1,..., n). Then q_\u003ci, k\u003e and h_\u003ci, k\u003e are placed alternately. The finite difference representations of Mahaffy\u0027s model are q_\u003ci, k\u003e=-{(h_\u003ci, k\u003e -h_\u003ci-1,k\u003e)/\u0026xutri;x}^n{(h_\u003ci, k\u003e+h_\u003ci-1,k\u003e)/2+(z_\u003coi\u003e+z_\u003coi\u003e^-_1)/2}^\u003cn+2\u003e and h_\u003ci, k+1\u003e=h_\u003ci, k\u003e+\u0026xutri;t{b-(q_\u003ci+1,k\u003e-q_\u003ci, k\u003e)/\u0026xutri;x}. If i\u0026xutri;x \u0026isins; Ω_2,mq_\u003ci, k\u003e is used instead of q_\u003ci, k\u003e. Boundary conditions are q_\u003c0,k\u003e=(-1)^n q_\u003c1,k\u003e and h_\u003cn, k\u003e=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\u0027s model, we multiply the weighting function W_l and integrate in the interior region Ω and apply Green\u0027s theorem, \u0026lmoust;_Ω k\u0026xdtri;h・\u0026xdtri;W_ldΩ-\u0026lmoust;_\u003c∂Ω\u003ek (∂h/∂n) W_ldГ=\u0026lmoust;_Ω(b-∂h/∂t) W_ldΩ, where ∂h/∂n=\u0026xdtri;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_\u003cl, m\u003e (h)=\u0026lmoust;_Ω k{(∂N_m/∂x)(∂N_l/∂x)+(∂N_m/∂y)(∂N_l/∂y)}dΩ-\u0026lmoust;_\u003c∂Ω\u003ek(∂N_m/∂n) N_ldГ, C_\u003cl, m\u003e=\u0026lmoust;_ΩN_mN_ldΩ, \u0026fnof;_l(h)=\u0026lmoust;_ΩbN_ldΩ, K=(K_\u003cl, m\u003e)_\u003cl, m=1,..., M, \u003e C=(C_\u003cl, m\u003e)_\u003cl, m=1,..., M\u003e and f=(\u0026fnof;_\u003c1,..., \u003e\u0026fnof;_M)^T. Then we can write the integral equation as K(h)h+C(∂h/∂t)=f(h). We apply the backward difference method over time, and define h^\u003c(n)\u003e=h(n\u0026xutri;t), K(h^\u003c(n)\u003e)h^\u003c(n)\u003e+C{(h^\u003c(n)\u003e-h^\u003c(n-1)\u003e)/\u0026xutri;t}=f(h^\u003c(n)\u003e). When h^\u003c(n-1)\u003e is solved, h^\u003c(n)\u003e can be solved by an iterative method, substituting an initial value into h^\u003c(n)\u003e. [numerical formula] and K_\u003cl, m\u003e (h) are defined when using Ω^e instead of Ωin K_\u003cl, m\u003e (h) C_\u003cl, m\u003e and \u0026fnof;_l (h) respectively. Then [numerical formula], and [numerical formula]. Here, [numerical formula] if l, m \u0026notin; Ω^e. Letting [numerical formula], [numerical formula] and [numerical formula], we calculate K^e, C^e and f^e for each e at first, then find K, C and f. The two dimensional scheme was applied to the Shirase drainage basin, and the three dimensional to the entire Antarctic ice sheet. The results seem to be satisfactory, although further improvements are to be carried out.", "subitem_description_type": "Other"}]}, "item_1_identifier_registration": {"attribute_name": "ID登録", "attribute_value_mlt": [{"subitem_identifier_reg_text": "10.15094/00003865", "subitem_identifier_reg_type": "JaLC"}]}, "item_1_publisher_22": {"attribute_name": "出版者", "attribute_value_mlt": [{"subitem_publisher": "National Institute of Polar Research"}]}, "item_1_source_id_13": {"attribute_name": "雑誌書誌ID", "attribute_value_mlt": [{"subitem_source_identifier": "AA10756213", "subitem_source_identifier_type": "NCID"}]}, "item_1_text_10": {"attribute_name": "著者所属(英)", "attribute_value_mlt": [{"subitem_text_language": "en", "subitem_text_value": "National Research Institute for Earth Science and Disaster Prevention"}, {"subitem_text_language": "en", "subitem_text_value": "Institute for Hydrospheric-Atmospheric Sciences, Nagoya University"}]}, "item_1_text_3": {"attribute_name": "記事種別(英)", "attribute_value_mlt": [{"subitem_text_language": "en", "subitem_text_value": "ABSTRACT"}]}, "item_files": {"attribute_name": "ファイル情報", "attribute_type": "file", "attribute_value_mlt": [{"accessrole": "open_date", "date": [{"dateType": "Available", "dateValue": "1994-11-01"}], "displaytype": "detail", "download_preview_message": "", "file_order": 0, "filename": "KJ00000767973.pdf", "filesize": [{"value": "163.2 kB"}], "format": "application/pdf", "future_date_message": "", "is_thumbnail": false, "licensetype": "license_6", "mimetype": "application/pdf", "size": 163200.0, "url": {"label": "KJ00000767973", "url": "https://nipr.repo.nii.ac.jp/record/3865/files/KJ00000767973.pdf"}, "version_id": "27e785ad-53b0-47c3-8245-9cdd56c1ff58"}]}, "item_language": {"attribute_name": "言語", "attribute_value_mlt": [{"subitem_language": "eng"}]}, "item_resource_type": {"attribute_name": "資源タイプ", "attribute_value_mlt": [{"resourcetype": "departmental bulletin paper", "resourceuri": "http://purl.org/coar/resource_type/c_6501"}]}, "item_title": "DEVELOPMENT OF A COMPUTER SIMULATION SCHEME FOR TWO AND THREE DIMENSIONAL ICE SHEET DYNAMICS MODELS", "item_titles": {"attribute_name": "タイトル", "attribute_value_mlt": [{"subitem_title": "DEVELOPMENT OF A COMPUTER SIMULATION SCHEME FOR TWO AND THREE DIMENSIONAL ICE SHEET DYNAMICS MODELS"}]}, "item_type_id": "1", "owner": "4", "path": ["532"], "permalink_uri": "https://doi.org/10.15094/00003865", "pubdate": {"attribute_name": "公開日", "attribute_value": "1994-11-01"}, "publish_date": "1994-11-01", "publish_status": "0", "recid": "3865", "relation": {}, "relation_version_is_last": true, "title": ["DEVELOPMENT OF A COMPUTER SIMULATION SCHEME FOR TWO AND THREE DIMENSIONAL ICE SHEET DYNAMICS MODELS"], "weko_shared_id": 4}
DEVELOPMENT OF A COMPUTER SIMULATION SCHEME FOR TWO AND THREE DIMENSIONAL ICE SHEET DYNAMICS MODELS
https://doi.org/10.15094/00003865
https://doi.org/10.15094/00003865d2e02400-bde1-46d4-805a-54c92c2c90e2
名前 / ファイル | ライセンス | アクション |
---|---|---|
KJ00000767973 (163.2 kB)
|
Item type | 紀要論文(ELS) / Departmental Bulletin Paper(1) | |||||
---|---|---|---|---|---|---|
公開日 | 1994-11-01 | |||||
タイトル | ||||||
タイトル | DEVELOPMENT OF A COMPUTER SIMULATION SCHEME FOR TWO AND THREE DIMENSIONAL ICE SHEET DYNAMICS MODELS | |||||
言語 | ||||||
言語 | eng | |||||
資源タイプ | ||||||
資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||
資源タイプ | departmental bulletin paper | |||||
ID登録 | ||||||
ID登録 | 10.15094/00003865 | |||||
ID登録タイプ | JaLC | |||||
ページ属性 | ||||||
内容記述タイプ | Other | |||||
内容記述 | P(論文) | |||||
記事種別(英) | ||||||
en | ||||||
ABSTRACT | ||||||
論文名よみ | ||||||
その他のタイトル | DEVELOPMENT OF A COMPUTER SIMULATION SCHEME FOR TWO AND THREE DIMENSIONAL ICE SHEET DYNAMICS MODELS | |||||
著者名よみ |
カワイ, シンイチ
× カワイ, シンイチ× ナカワ, マサヨシ |
|||||
著者名(英) |
KAWAI, Shinichi
× KAWAI, Shinichi× NAKAWO, Masayoshi |
|||||
著者所属(英) | ||||||
en | ||||||
National Research Institute for Earth Science and Disaster Prevention | ||||||
著者所属(英) | ||||||
en | ||||||
Institute for Hydrospheric-Atmospheric Sciences, Nagoya University | ||||||
抄録(英) | ||||||
内容記述タイプ | Other | |||||
内容記述 | 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_<i, k>=q((i-1/2) △x, k△t) (i=0,1,..., n+1) and h_<i, k>=h (i△x, k△t)(i=0,1,..., n), z_<0i>=z_0 (i△x) (i=0,1,..., n). Then q_<i, k> and h_<i, k> are placed alternately. The finite difference representations of Mahaffy's model are q_<i, k>=-{(h_<i, k> -h_<i-1,k>)/△x}^n{(h_<i, k>+h_<i-1,k>)/2+(z_<oi>+z_<oi>^-_1)/2}^<n+2> and h_<i, k+1>=h_<i, k>+△t{b-(q_<i+1,k>-q_<i, k>)/△x}. If i△x ⋴ Ω_2,mq_<i, k> is used instead of q_<i, k>. 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,..., >ƒ_M)^T. Then we can write the integral equation as K(h)h+C(∂h/∂t)=f(h). We apply the backward difference method over time, and define h^<(n)>=h(n△t), K(h^<(n)>)h^<(n)>+C{(h^<(n)>-h^<(n-1)>)/△t}=f(h^<(n)>). When h^<(n-1)> is solved, h^<(n)> can be solved by an iterative method, substituting an initial value into h^<(n)>. [numerical formula] and K_<l, m> (h) are defined when using Ω^e instead of Ωin K_<l, m> (h) C_<l, m> and ƒ_l (h) respectively. Then [numerical formula], and [numerical formula]. Here, [numerical formula] if l, m ∉ Ω^e. Letting [numerical formula], [numerical formula] and [numerical formula], we calculate K^e, C^e and f^e for each e at first, then find K, C and f. The two dimensional scheme was applied to the Shirase drainage basin, and the three dimensional to the entire Antarctic ice sheet. The results seem to be satisfactory, although further improvements are to be carried out. | |||||
雑誌書誌ID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AA10756213 | |||||
書誌情報 |
Proceedings of the NIPR Symposium on Polar Meteorology and Glaciology 巻 8, p. 208, 発行日 1994-11 |
|||||
出版者 | ||||||
出版者 | National Institute of Polar Research |