Remote sensing observations from satellites and global biogeochemical models have combined to revolutionize the study of ocean biogeochemical cycling, but comparing the two data streams to each other and across time remains challenging due to the strong spatial-temporal structuring of the ocean. Here, we show that the Wasserstein distance provides a powerful metric for harnessing these structured datasets for better marine ecosystem and climate predictions. Wasserstein distance complements commonly used point-wise difference methods such as the root mean squared error, by quantifying differences in terms of spatial displacement in addition to magnitude. As a test case we consider Chlorophyll (a key indicator of phytoplankton biomass) in the North-East Pacific Ocean, obtained from model simulations, in situ measurements, and satellite observations. We focus on two main applications: 1) Comparing model predictions with satellite observations, and 2) temporal evolution of Chlorophyll both seasonally and over longer time frames. Wasserstein distance successfully isolates temporal and depth variability and quantifies shifts in biogeochemical province boundaries. It also exposes relevant temporal trends in satellite Chlorophyll consistent with climate change predictions. Our study shows that optimal transport vectors underlying Wasserstein distance provide a novel visualization tool for testing models and better understanding temporal dynamics in the ocean.
翻译:卫星和全球生物地球化学模型的遥感观测相结合,使海洋生物地球化学循环的研究发生了革命性的变化,但是由于海洋空间时空结构的强大,将两个数据流相互比较并随着时间推移仍然具有挑战性。在这里,我们表明,瓦瑟斯坦距离为利用这些结构化数据集改善海洋生态系统和气候预测提供了强大的衡量标准。 瓦瑟斯坦距离补充了常用的点向差异方法,如根平均正方差,将空间迁移的差异除大小外加以量化。作为一个试验案例,我们考虑东北太平洋的氯酚(浮游植物生物的重要指标),这是从模拟模型、实地测量和卫星观测中获得的。我们侧重于两个主要应用:(1) 模型预测与卫星观测和气候预测的比较,和(2) 叶绿素的季节性和时间框架的暂时演变。 瓦瑟斯坦距离成功地将时间和深度变异性与生物化学地区边界的变异性量化。它还暴露了卫星叶绿素(浮游生物量生物量)的相关时间趋势(一个关键指标),这是从模拟模拟、实地测量和卫星观测观测中得出的。 我们的视野变异性模型展示了最佳的大气变异性模型。