We present a new optimization-based property-preserving algorithm for passive tracer transport. The algorithm utilizes a semi-Lagrangian approach based on incremental remapping of the mass and the total tracer. However, unlike traditional semi-Lagrangian schemes, which remap the density and the tracer mixing ratio through monotone reconstruction or flux correction, we utilize an optimization-based remapping that enforces conservation and local bounds as optimization constraints. In so doing we separate accuracy considerations from preservation of physical properties to obtain a conservative, second-order accurate transport scheme that also has a notion of optimality. Moreover, we prove that the optimization-based algorithm preserves linear relationships between tracer mixing ratios. We illustrate the properties of the new algorithm using a series of standard tracer transport test problems in a plane and on a sphere.
A common approach for the development of partitioned schemes employing different time integrators on different subdomains is to lag the coupling terms in time. This can lead to accuracy issues, especially in multistage methods. In this article, we present a novel framework for partitioned heterogeneous time‐integration methods, which allows the coupling of arbitrary multistage and multistep methods without reducing their order of accuracy. At the core of our approach are accurate estimates of the interface flux obtained from the Schur complement of an auxiliary monolithic system . We use these estimates to construct a polynomial‐in‐time approximation of the interface flux over the current time coupling window. This approximation provides the interface boundary conditions necessary to decouple the subdomain problems at any point within the coupling window. In so doing our framework enables a flexible choice of time‐integrators for the individual subproblems without compromising the time‐accuracy at the coupled problem level. This feature is the main distinction between our framework and other approaches. To demonstrate the framework, we construct a family of partitioned heterogeneous time‐integration methods, combining multistage and multistep methods, for a simplified tracer transport component of the coupled air‐sea system in Earth system models. We report numerical tests evaluating accuracy and flux conservation for different pairs of time‐integrators from the explicit Runge‐Kutta and Adams‐Moulton families.
For decades, Arctic temperatures have increased twice as fast as average global temperatures. As a first step toward quantifying parametric uncertainty in Arctic climate, we performed a variance-based global sensitivity analysis (GSA) using a fully coupled, ultra-low resolution (ULR) configuration of version 1 of the U.S. Department of Energy's Energy Exascale Earth System Model (E3SMv1). Specifically, we quantified the sensitivity of six quantities of interests (QOIs), which characterize changes in Arctic climate over a 75 year period, to uncertainties in nine model parameters spanning the sea ice, atmosphere, and ocean components of E3SMv1. Sensitivity indices for each QOI were computed with a Gaussian process emulator using 139 random realizations of the random parameters and fixed preindustrial forcing. Uncertainties in the atmospheric parameters in the Cloud Layers Unified by Binormals (CLUBB) scheme were found to have the most impact on sea ice status and the larger Arctic climate. Our results demonstrate the importance of conducting sensitivity analyses with fully coupled climate models. The ULR configuration makes such studies computationally feasible today due to its low computational cost. When advances in computational power and modeling algorithms enable the tractable use of higher-resolution models, our results will provide a baseline that can quantify the impact of model resolution on the accuracy of sensitivity indices. Moreover, the confidence intervals provided by our study, which we used to quantify the impact of the number of model evaluations on the accuracy of sensitivity estimates, have the potential to inform the computational resources needed for future sensitivity studies.
For decades, Arctic temperatures have increased twice as fast as average global temperatures. As a first step toward quantifying parametric uncertainty in Arctic climate, we performed a variance-based global sensitivity analysis (GSA) using a fully coupled, ultra-low resolution (ULR) configuration of version 1 of the U.S. Department of Energy's Energy Exascale Earth System Model (E3SMv1). Specifically, we quantified the sensitivity of six quantities of interests (QOIs), which characterize changes in Arctic climate over a 75 year period, to uncertainties in nine model parameters spanning the sea ice, atmosphere, and ocean components of E3SMv1. Sensitivity indices for each QOI were computed with a Gaussian process emulator using 139 random realizations of the random parameters and fixed preindustrial forcing. Uncertainties in the atmospheric parameters in the Cloud Layers Unified by Binormals (CLUBB) scheme were found to have the most impact on sea ice status and the larger Arctic climate. Our results demonstrate the importance of conducting sensitivity analyses with fully coupled climate models. The ULR configuration makes such studies computationally feasible today due to its low computational cost. When advances in computational power and modeling algorithms enable the tractable use of higher-resolution models, our results will provide a baseline that can quantify the impact of model resolution on the accuracy of sensitivity indices. Moreover, the confidence intervals provided by our study, which we used to quantify the impact of the number of model evaluations on the accuracy of sensitivity estimates, have the potential to inform the computational resources needed for future sensitivity studies.
In September of 2020, Arctic sea ice extent was the second-lowest on record. State of the art climate prediction uses Earth system models (ESMs), driven by systems of differential equations representing the laws of physics. Previously, these models have tended to underestimate Arctic sea ice loss. The issue is grave because accurate modeling is critical for economic, ecological, and geopolitical planning. We use machine learning techniques, including random forest regression and Gini importance, to show that the Energy Exascale Earth System Model (E3SM) relies too heavily on just one of the ten chosen climatological quantities to predict September sea ice averages. Furthermore, E3SM gives too much importance to six of those quantities when compared to observed data. Identifying the features that climate models incorrectly rely on should allow climatologists to improve prediction accuracy.
We use a nascent data-driven causal discovery method to find and compare causal relationships in observed data and climate model output. We consider ten different features in the Arctic climate collected from public databases on observational and Energy Exascale Earth System Model (E3SM) data. In identifying and analyzing the resulting causal networks, we make meaningful comparisons between observed and climate model interdependencies. This work demonstrates our ability to apply the PCMCI causal discovery algorithm to Arctic climate data, that there are noticeable similarities between observed and simulated Arctic climate dynamics, and that further work is needed to identify specific areas for improvement to better align models with natural observations.