  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.
