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  1. The western Arctic Ocean is rapidly acidifying due to sea ice loss. 
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  2. The Gaussian-smoothed optimal transport (GOT) framework, recently proposed by Goldfeld et al., scales to high dimensions in estimation and provides an alternative to entropy regularization. This paper provides convergence guarantees for estimating the GOT distance under more general settings. For the Gaussian-smoothed $p$-Wasserstein distance in $d$ dimensions, our results require only the existence of a moment greater than $d + 2p$. For the special case of sub-gamma distributions, we quantify the dependence on the dimension $d$ and establish a phase transition with respect to the scale parameter. We also prove convergence for dependent samples, only requiring a condition on the pairwise dependence of the samples measured by the covariance of the feature map of a kernel space. A key step in our analysis is to show that the GOT distance is dominated by a family of kernel maximum mean discrepancy (MMD) distances with a kernel that depends on the cost function as well as the amount of Gaussian smoothing. This insight provides further interpretability for the GOT framework and also introduces a class of kernel MMD distances with desirable properties. The theoretical results are supported by numerical experiments.The Gaussian-smoothed optimal transport (GOT) framework, recently proposed by Goldfeld et al., scales to high dimensions in estimation and provides an alternative to entropy regularization. This paper provides convergence guarantees for estimating the GOT distance under more general settings. For the Gaussian-smoothed $p$-Wasserstein distance in $d$ dimensions, our results require only the existence of a moment greater than $d + 2p$. For the special case of sub-gamma distributions, we quantify the dependence on the dimension $d$ and establish a phase transition with respect to the scale parameter. We also prove convergence for dependent samples, only requiring a condition on the pairwise dependence of the samples measured by the covariance of the feature map of a kernel space. A key step in our analysis is to show that the GOT distance is dominated by a family of kernel maximum mean discrepancy (MMD) distances with a kernel that depends on the cost function as well as the amount of Gaussian smoothing. This insight provides further interpretability for the GOT framework and also introduces a class of kernel MMD distances with desirable properties. The theoretical results are supported by numerical experiments. 
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  3. null (Ed.)
  4. Abstract

    The acidification of coastal waters is distinguished from the open ocean because of much stronger synergistic effects between anthropogenic forcing and local biogeochemical processes. However, ocean acidification research is still rather limited in polar coastal oceans. Here, we present a 17‐year (2002–2019) observational data set in the Chukchi Sea to determine the long‐term changes in pH and aragonite saturation state (Ωarag). We found that pH and Ωaragdeclined in different water masses with average rates of −0.0047 ± 0.0026 years−1and −0.017 ± 0.009 years−1, respectively, and are ∼2–3 times faster than those solely due to increasing atmospheric CO2. We attributed the rapid acidification to the increased dissolved inorganic carbon owing to a combination of ice melt‐induced increased atmospheric CO2invasion and subsurface remineralization induced by a stronger surface biological production as a result of the increased inflow of the nutrient‐rich Pacific water.

     
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