Water renewal timescales, namely age, residence time, and exposure time, which are defined in accordance with the Constituent-oriented Age and Residence time Theory (CART), are computed by means of the unstructured-mesh, finite element model Second-generation Louvain-la-Neuve Ice-ocean Model (SLIM) in the Mahakam Delta (Borneo Island, Indonesia). Two renewing water types, i.e., water from the upstream boundary of the delta and water from both the upstream and the downstream boundaries, are considered, and their age is calculated as the time elapsed since entering the delta. The residence time of the water originally in the domain (i.e., the time needed to hit an open boundary for the first time) and the exposure time (i.e., the total time spent in the domain of interest) are then computed. Simulations are performed for both low and high flow conditions, revealing that (i) age, residence time, and exposure time are clearly related to the river volumetric flow rate, and (ii) those timescales are of the order of one spring-neap tidal cycle. In the main deltaic channels, the variation of the diagnostic timescales caused by the tide is about 35% of their averaged value. The age of renewing water from the upstream boundary of the delta monotonically increases from the river mouth to the delta front, while the age of renewing water from both the upstream and the downstream boundaries monotonically increases from the river mouth and the delta front to the middle delta. Variations of the residence and the exposure times coincide with the changes of the flow velocity, and these timescales are more sensitive to the change of flow dynamics than the age. The return coefficient, which measures the propensity of water to re-enter the domain of interest after leaving it for the first time, is of about 0.3 in the middle region of the delta.

中文翻译：

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印度尼西亚 Mahakam 三角洲水更新时间尺度的数值模拟

水更新时间尺度，即年龄、停留时间和暴露时间，根据成分导向的年龄和停留时间理论 (CART) 定义，通过非结构化网格、有限元模型 Second generation Louvain 计算-la-Neuve 冰海模型 (SLIM) 在 Mahakam Delta（印度尼西亚婆罗洲岛）。考虑了两种更新水类型，即来自三角洲上游边界的水和来自上游和下游边界的水，它们的年龄计算为自进入三角洲以来经过的时间。然后计算水最初在域中的停留时间（即第一次到达开放边界所需的时间）和暴露时间（即在感兴趣的域中花费的总时间）。对低流量和高流量条件进行了模拟，表明 (i) 年龄、停留时间和暴露时间与河流体积流量明显相关，并且 (ii) 这些时间尺度大约是一个春季小潮循环。在主要三角洲河道中，潮汐引起的诊断时间尺度变化约为平均值的35%。三角洲上游边界更新水年龄从河口到三角洲前缘单调增加，而上下游边界更新水年龄从河口和三角洲前缘向中部单调增加三角洲。停留时间和暴露时间的变化与流速的变化一致，并且这些时间尺度对流动动力学的变化比年龄更敏感。衡量水首次离开后重新进入感兴趣域的倾向的返回系数在三角洲中部约为 0.3。