However, no matter how good the record from fixed tide gauges, they can only tell us what is happening on the coast. While that's arguably the most important for mankind, it's hardly a global picture.
The other approach that we can take is satellite observations. Radar altimeters on satellites can, and do, measure sea level worldwide to a precision of a few centimetres or better. This is a recent mission for this purpose (there may have been others since - I'm not an expert). The level of accuracy here is not as good, but it can be improved statistically through a large number of measurements.
The greater difficulty with satellite altimetry is removing the tides, because the satellites are always moving over the earth's surface and so can only measure any one location at relatively infrequent intervals. Consequently, some sophisticated global tidal models are used with data provided by the satellites to (a) improve the models, for people who want to predict tides, and (b) use the tides from the models to remove the tides from the satellite measurements, leaving just longer-term changes in sea level.
I think part of the intent of your question is "people quote changes in sea level of millimetres or centimetres per year, yet surely the measurements are not this accurate?". Well, satellite measurements aren't, though local ones might be, but remember that we're measuring for more than just one year. One approach might be to look at a ten- or twenty-year trend, and work out the average change per year from that.
通过一些机制，有些是直接的，有些是间接的。各种政府机构，如美国国家海洋和大气管理局运营着沿海潮汐站，测量当地的海平面高度。全世界大约有一千个这样的地方。除了这些官方潮汐站，还有更多的私人潮汐站，比如海上钻井平台上的潮汐站。
其他测量结果来自浮标，有些是锚定的，有些是漂浮的。光是ARGO浮标就有将近5000个。ARGO浮标测量不同深度的温度。由于温度较高的海水密度小于温度较低的海水，海洋温度上升是海平面上升的一个关键因素，约占海平面上升总量的1/3。然而，其他的测量数据来自太空。其余2/3的海平面上升是由于海洋质量的增加。这种增加的质量可以通过GRACE卫星等高精度重力实验来测量。 Those precise measurements in the changes in Earth's gravity field enables precise orbit determination of other satellites, some of which carry radar altimeters. Those altimeter readings, coupled with high precision orbit determinations, provide yet another mechanism for assessing sea level change.
(添加这个作为单独的答案，因为它回答了问题的不同部分——我第一次回答时不存在……)
要理解为什么海平面上升10厘米就会很重要:
想象一个地方偶尔会发生洪水。也许一年只有一次，或者更少。现在想想它有多频繁地发生洪水——水停在离墙顶只有5厘米的地方。这些情况不会以同样的方式报道，但它们可能比真正发生洪水的时候要频繁得多。因此，海平面的小幅上升可能会对许多沿海地区产生严重影响——尤其是在地势较低的国家，如荷兰或孟加拉国(其中一个国家有能力提高城墙;另外，请记住，虽然我们现在处理的是毫米/年，但许多气候科学家所关心的不是几厘米-而是几米米。在这个水平上，美国大部分沿海城市都被淹没了