摘 要
本研究主要的目的在於使用GEOSECS已發表過的鐳-226及溫鹽‥等數據，企圖在北太平洋沿著300N從東到西排列的十個測站中，利用一維及二維擴散-對流模式來估計若干重要參數。
由於模式在建立時，常有邊界條件的限制，使得計算結果與示蹤劑在實際海洋中的分佈爭議性甚大。由擴散-對流模式及位溫資料求得本研究區的Z*，大致介於0.8 km至1.0 km；JBa/w由Ba剖面數據求得，大致介於0.0020至0.0064 nM/kg/m之間。
在本研究測線上，四個測站含有Ba剖面數據，由這些數據看出226Ra和Ba在深層水以上有相當良好的線性關係；其斜率為0.22 dpm/100nM，相當之莫耳比為4.4 ×10-9，其截距在Ba軸上為0.48 nM/kg。
Ra-Ba在深層水以上會有良好的線性關係，初步推斷，是因為方程式中，（ＪRa－λＣRa）約為定值，可以改寫方程式和Ba的擴散-對流模式相同，因此觀測到的Ra和Ba會呈線性相關。
在四個含有Ba剖面數據的測站，可以藉（ ）/ 為定值，經由模式的調適，求出各項參數值。所求的湧升速率(w)，在204站為3.8 m/yr；212站為4.8 m/yr；226站為3.5 m/yr；224站為1.2 m/yr。此結果大致與在太平洋深層水利用其他方法求得之湧升速率（1至12 m/yr）吻合。
226Ra剖面數據，經一維擴散-對流模式調適之後，發現現場生產率（J）和湧升速率（w）的解會呈負相關，與文獻報導一致。
在靠近東北太平洋的測站中，深層水以下有”超量”226Ra的分佈情形，最大值由東向西延伸，直到西北太平洋靠近日本完全消失， Chung and Craig(1980)利用水平一維模式對”超量”226Ra所估的水平擴散係數Kh=5 ×105 cm2/s。本研究使用有限差分法，對位溫做二維擴散對流模式調適，得出東西向擴散係數Kx，在1000m至3000m為4.58 ×105 cm2/s；在1000m至4000m為4.82 ×105 cm2/s。兩種方法所求的水平擴散係數大致相同。

A total of 10 vertical 226Ra profiles from the North Pacific was published as part of the GEOSECS program. These profiles are located on an east-west section along ~300N. The purpose of this thesis is to use one-dimensional and two-dimensional diffusion-advection models to estimate some important geochemical parameters.
There are some discrepancies between the modeling results and the observed tracer distributions due to restrictions on end-members in the models. Fitting the observed data to the model, one obtains values of the Z* between 0.8 and 1.0 km from potential temperature and that of JBa/w between 0.0020 and 0.0064 nM/kg/m from Ba.
Where Ba profiles are available, the corresponding 226Ra profiles are similar from the surface to the deep water, showing a linear correlation with a slope at 0.22 dpm/100nM or 4.4×10-9 for the Ra/Ba molal ratio. The slope has an intercept of 0.48 nM/kg on the Ba axis.
That 226Ra is linearly correlated with Ba from surface water to deep water is probably because algebraic sum of the production term and the radioactive decay is nearly constant. Thus the revised model has a form equivalent to that for Ba.
Where Ba profiles are available, one can fit the observed data to the model to obtain the needed parameters with (JRa-λCRa)/JBa as a constant. The upwelling velocity, w, obtained from model calculations on the Ba profiles is: 3.8 m/yr at 204; 4.8 m/yr at 212; 3.5 m/yr at 226, 1.2 m/yr at 224. These values are consistent with those (1 to 12m/yr) reported for the Pacific deep water based on other methods.
Fitting 226Ra profile data to the vertical one-dimensional diffusion-advection model for the in-situ production rate, J, and the associated upwelling velocity, w, one finds that J and w are coupled with a negative correlation. This is consistent with that reported in the literature.
Profiles from the northeast Pacific show a deep Ra maximum, with an “excess” which extends westward while decreasing and finally vanishing in the northwest Pacific near Japan. A horizontal diffusivity of 5 ×105 cm2/s was obtained based on this “excess” 226Ra with a horizontal 1-D model by Chung and Craig (1980). A numerical finite-difference method is applied to the 2-D model fitting on the potential temperature data for the horizontal diffusivity, Kx. A Kx of 4.58 ×105 cm2/s is obtained within the depth range of 1000m to 3000m. The value is 4.82 ×105 cm2/s for the depth range from 1000m to 4000m. These two approaches yield nearly identical results.

目 錄
一、緒論………………………………………………………………....1
二、數值模式……………………………………………………………7
2.1 擴散－對流模式………………………………………………….7
2.2 226Ra－Ba關係模式……………………………………………...11
2.3 226Ra “超量”模式……….………………………………………..13
三、數值方法………………………………………………………..…15
3.1 最小平方法求迴歸…………………………………...…………15
3.2 Gauss-Newton 法…………………………………………..……17
3.3 有限差分法……………………………………………………...19
3.4 複相關與複回歸………………………………………………...21
四、結果與討論………………………………………………………..24
4.1水文資料描述……………………………………………………24
4.2 226Ra-Ba特性描述……………………………………………….32
4.3一維模式解法之比較與合理性探討……………………………35
4.4 調適結果的優劣取捨…………………………………………...40
4.5 一維模式計算…………………………………………………...42
4.5.1 溫度、鹽度剖面分析………………………………………44
4.5.2 Ba剖面數據分析……………………………………………47
4.5.3 226Ra剖面數據分析…………………………………………48
4.6 再論226Ra-Ba關係…………………..………………………….54
4.7 二維模式計算…………………………………………………...58
4.7.1 溫度、鹽度資料分析………………………………………59
4.7.2 226Ra資料分析………………………………………………62
4.7.3二維模式計算討論.…………………………………………64
五、結論………………………………………………………………..65
六、附錄………………………………………………………………..68
參考文獻………………………………………………………………..88
中文部分……………………………………………………………..88
英文部分……………………………………………………………..89

圖 目 錄

圖4-1本文使用之GEOSECS測站位置圖.…………………………..25
圖4-2 北太平洋GEOSECS東西向測線位溫(θ)剖面圖……………26
圖4-3 北太平洋GEOSECS東西向測線鹽度剖面圖..……………….27
圖4-4 北太平洋測線位溫(θ)等值圖…………………………………28
圖4-5 北太平洋測線鹽度等值圖……………………………………..28
圖4-6 十個測站的位溫鹽度圖………………………………………..29
圖4-7 十個測站水深1000~4000m之間各站的θ-S關係…………..31
圖4-8 各測站之226Ra-Ba關係圖……..………………………………33
圖4-9 表水至3500m之間，四測站之共同226Ra-Ba關係圖……….…33
圖4-10 “超量”鐳-226在十個測站中的分佈…………………………..43
圖4-11 226Ra模式解得J和w關係……..……………………………..51


表 目 錄

表2-1 一維擴散-對流模式之特解…………………………………….10
表4-1 一維擴散-對流模式不含邊界條件之一般解………………….35
表4-2 有邊界條件調適結果…………………………………………..45
表4-3 無邊界條件調適結果…………………………………………..45
表4-4無邊界條件調適結果……………………………………………47
表4-5 Ba模式的解代入226Ra模式的結果……………………………50
表4-6 226Ra模式的估計結果…………………………………………..50
表4-7 將λΔC忽略之後的226Ra模式調適…………………………56
表4-8 用推論的JRa/JBa關係重新求解…………………………………56
表4-9 各個測站的經度………………………………………………..59
表4-10 位溫在十個站位十一個深度的估計值(℃)…………………..59
表4-11 位溫在十個站位十六個深度的估計值(℃)…………………..60
表4-12位溫資料調適結果…….………………………………………61
表4-13 差補之後的網格點狀況………………………………………62
表6-1 GEOSECS已發表的201測站數據…………………………….68
表6-2 GEOSECS已發表的202測站數據…………………………….70
表6-3 GEOSECS已發表的204測站數據…………………………….72
表6-4 GEOSECS已發表的212測站數據…………………………….74
表6-5 GEOSECS已發表的213測站數據…………………………….76
表6-6 GEOSECS已發表的214測站數據……………………………..78
表6-7 GEOSECS已發表的226測站數據…………………………….80
表6-8 GEOSECS已發表的225測站數據…………………………….82
表6-9 GEOSECS已發表的223測站數據…………………………….84
表6-10 GEOSECS已發表的224測站數據……………………………86

中文部分
袁帝文，1997，應用數值方法，儒林出版社，第七章。
陳順宇，1996，統計學，華泰書局。

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