Abstract The 200 m-thick surface layer of the Arctic Ocean contains a lower salinity part in the Canadian Basin, receiving fresher water from the Pacific Ocean as well as rivers, and also a higher salinity part in the Eurasian Basin, receiving saltier water from the Greenland Sea. This surface layer receives atmospheric forcing, and also partially mixes with the subsurface layer. Thus, thermohaline circulation is a fundamental pattern, under the influences of mesoscale features ( ∼ 10 km) and small-scale plumes ( ∼ 1 km). The one-box model of the surface layer possesses a salinity-driven state, and also a convected state with the subsurface layer as another solution. The new modeling is proposed with a probability distribution function (PDF) on the temperature–salinity (T–S) plane, which can represent horizontal gradients and small scale features as well. The T–S distribution retains only the probabilities of different water types, while their locations are discarded. Time progressions of the PDF are calculated with mechanisms of box-mean progression, heterogeneity generation, horizontal mixing in the box and convection with the subsurface layer. As either the subsurface layer becomes fresher, or the heterogeneity is intensified, the solution near the salinity-driven state increases convection, shifting toward the convected state. The additional PDF box model is made for the Eurasian Basin, which receives fresher water from the Canadian Basin instead of the Pacific Ocean, and provides a more restricted solution with convection, mainly controlled by the fresher subsurface layer. The original PDF box model of the entire Arctic Ocean is extended to the wider horizontal variability case: i.e., the inflow from the Greenland Sea is distributed over the higher salinity portion only, and then, the lower salinity water from the Pacific Ocean is supplied to a particular T–S point, ( T p , S p ), mixing within the lower salinity portion only. The low salinity core is retained near ( T p , S p ), even though convection develops in the higher salinity portion. Thus, this advanced PDF box model is a useful tool to judge a high resolution basin-scale circulation model, whether small-scale plumes and mesoscale features play an important role on thermohaline circulation or not.

中文翻译：

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使用概率分布函数实现的盒模型复制具有水平变化的北冰洋表层 (PDF)

摘要 北冰洋表层 200 m 厚，加拿大海盆含盐度较低的部分，接收来自太平洋和河流的淡水；欧亚海盆含盐度较高的部分，接收来自太平洋和河流的咸水。格陵兰海。该地表层受到大气强迫，也部分地与地下层混合。因此，在中尺度特征（~10 公里）和小尺度羽流（~1 公里）的影响下，温盐环流是一种基本模式。表层的单盒模型具有盐度驱动状态，也具有对流状态，地下层作为另一种解决方案。新建模提出了温度-盐度 (T-S) 平面上的概率分布函数 (PDF)，它也可以表示水平梯度和小尺度特征。T-S 分布仅保留不同水类型的概率，而丢弃它们的位置。PDF 的时间进程是通过盒均值进程、异质性生成、盒内水平混合和与地下层对流的机制计算的。随着地下层变得更新鲜，或者不均匀性加剧，接近盐度驱动状态的溶液会增加对流，转向对流状态。额外的 PDF 框模型是为欧亚盆地制作的，它从加拿大盆地而不是太平洋接收更新鲜的水，并提供一个更受限制的解决方案，对流主要由更新鲜的地下层控制。整个北冰洋的原始PDF盒模型扩展到更广泛的水平变化情况：即来自格陵兰海的流入仅分布在较高盐度的部分，然后来自太平洋的较低盐度的水供应给一个特定的 T-S 点 (T p , S p )，仅在低盐度部分混合。低盐度核心保留在 (T p , Sp ) 附近，即使对流在较高盐度部分发展。因此，这种先进的 PDF 盒模型是判断高分辨率盆地尺度环流模型的有用工具，无论小尺度羽流和中尺度特征是否在温盐环流中发挥重要作用。然后，来自太平洋的低盐度水被供应到特定的 T-S 点（Tp，Sp），仅在低盐度部分混合。低盐度核心保留在 (T p , Sp ) 附近，即使对流在较高盐度部分发展。因此，这种先进的 PDF 盒模型是判断高分辨率盆地尺度环流模型的有用工具，无论小尺度羽流和中尺度特征是否在温盐环流中发挥重要作用。然后，来自太平洋的低盐度水被供应到特定的 T-S 点（Tp，Sp），仅在低盐度部分混合。低盐度核心保留在 (T p , Sp ) 附近，即使对流在较高盐度部分发展。因此，这种先进的 PDF 盒模型是判断高分辨率盆地尺度环流模型的有用工具，无论小尺度羽流和中尺度特征是否在温盐环流中发挥重要作用。