Long-term behaviour of sea-level rise is an important factor in assessing the impact of climate change on multi-century timescales. Under the stabilisation scenario RCP4.5, Sterodynamic Sea-Level (SdynSL) and ocean density change in the CMIP5 models exhibit distinct patterns over the periods before and after Radiative Forcing (RF) stabilisation (2000–2070 vs. 2100–2300). The stabilisation pattern is more geographically uniform and involves deeper penetration of density change than the transient pattern. In RCP2.6, 4.5 and 8.5, the spatiotemporal evolution of SdynSL change can be approximated as a linear combination of the transient and stabilisation patterns. Specifically, SdynSL change is dominated by the transient pattern when RF increases rapidly, but it is increasingly affected by the stabilisation pattern once RF starts to stabilise. The growth of the stabilisation pattern could persist for centuries after RF ceases increasing. The evolving patterns of SdynSL change can also be approximated as a linear system's responses (characterised by its Green’s function) to time-dependent boundary conditions. By examining SdynSL change simulated in linear system models with different estimates of Green's functions, we find that both the climatological ocean circulation and the ocean's dynamical response to RF play a role in shaping the patterns of SdynSL change. The linear system model is more accurate than the univariate pattern scaling in emulating the CMIP5 SdynSL change beyond 2100. The emergence of the stabilisation pattern leads to a 1–10% decrease in the ocean's expansion efficiency of heat over 2000–2300 in RCP2.6 and 4.5.

海平面上升的长期行为是评估气候变化对多世纪时间尺度影响的重要因素。在RCP4.5稳定情景下，CMIP5模型中的动能海平面（SdynSL）和海洋密度变化在辐射强迫（RF）稳定前后（2000-2070年与2100-2300年）之间表现出不同的模式。稳定模式在地理上更加统一，并且比瞬态模式更深入地渗透密度变化。在RCP2.6、4.5和8.5中，SdynSL变化的时空演变可以近似为瞬态和稳定模式的线性组合。具体而言，当RF快速增加时，SdynSL的变化主要由瞬态模式决定，但是一旦RF开始稳定，它就会越来越受到稳定模式的影响。RF停止增加后，稳定模式的增长可能会持续几个世纪。SdynSL变化的演变模式也可以近似为线性系统对时间相关边界条件的响应（以格林函数为特征）。通过检查在线性系统模型中模拟的SdynSL变化（具有格林函数的不同估计），我们发现气候海洋环流和海洋对RF的动态响应都在塑造SdynSL变化模式中起作用。在模拟2100年以后的CMIP5 SdynSL变化时，线性系统模型比单变量模式缩放更准确。稳定模式的出现导致RCP2.6中2000–2300年海洋热膨胀效率降低1–10％。和4.5。