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The familiar divergence and Kelvin–Stokes theorem are generalized by a tensor-valued identity that relates the volume integral of the gradient of a vector field to the integral over the bounding surface of the tensor product of the vector field with the exterior normal. The importance of this long-established yet relatively little-known result is discussed. In flat two-dimensional space, it reduces to a relationship between an integral over an area and that over its bounding curve, combining the two-dimensional divergence and Kelvin–Stokes theorems together with two related theorems involving the strain, as is shown through a decomposition using a suitable tensor basis. A fluid dynamical application to oceanic observations along the trajectory of a moving platform is given. The potential extension of the generalized two-dimensional identity to curved surfaces is considered and is shown not to hold. Finally, the paper includes a substantial background section on tensor analysis, and presents results in both symbolic notation and index notation in order to emphasize the correspondence between these two notational systems. 

During polar winter, refreezing of exposed ocean areas results in the rejection of brine, i.e., salt-enriched plumes of water, a source of available potential energy that can drive ocean instabilities. As this process is highly localized, and driven by sea ice physics, not gradients in oceanic or atmospheric buoyancy, it is not currently captured in modern climate models. This study aims to understand the energetics and lateral transfer of density at a semi-infinite, instantaneously-opened and continuously re-freezing sea ice edge through a series of high resolution model experiments. We show that kilometer-scale submesoscale eddies grow from baroclinic instabilities via an inverse energy cascade. These eddies meander along the ice edge and propagate laterally. The lateral transfer of buoyancy by eddies is not explained by existing theories. We isolate the fundamental forcing-independent quantities driving lateral mixing, and discuss the implications for the overall strength of submesoscale activity in the Arctic Ocean.

 

This work evaluates the fidelity of various upper-ocean turbulence parameterizations subject to realistic monsoon forcing and presents a finite-time ensemble vector (EV) method to better manage the design and numerical principles of these parameterizations. The EV method emphasizes the dynamics of a turbulence closure multimodel ensemble and is applied to evaluate 10 different ocean surface boundary layer (OSBL) parameterizations within a single-column (SC) model against two boundary layer large-eddy simulations (LES). Both LES include realistic surface forcing, but one includes wind-driven shear turbulence only, while the other includes additional Stokes forcing through the wave-average equations that generate Langmuir turbulence. The finite-time EV framework focuses on what constitutes the local behavior of the mixed layer dynamical system and isolates the forcing and ocean state conditions where turbulence parameterizations most disagree. Identifying disagreement provides the potential to evaluate SC models comparatively against the LES. Observations collected during the 2018 monsoon onset in the Bay of Bengal provide a case study to evaluate models under realistic and variable forcing conditions. The case study results highlight two regimes where models disagree 1) during wind-driven deepening of the mixed layer and 2) under strong diurnal forcing.

 

Ocean model simulations show variability due to intrinsic chaos and external forcing (air‐sea fluxes, river input, etc.). It is important to estimate their contributions to total variability for attribution. Using variance to estimate variability might be unreliable due to non‐Gaussian higher statistical moments. We show the use of non‐parametric information theory metrics, Shannon entropy and mutual information, for measuring internal and forced variability in ocean models. These metrics are applied to spatially and temporally averaged data. The metrics delineate relative intrinsic to total variability in a wider range of circumstances than previous approaches based on variance ratios. The metrics are applied to (a) a synthetic ensemble of random vectors, (b) ocean component of a global climate (GFDL‐ESM2M) large ensemble, (c) ensemble of a realistic coastal ocean model. The information theory metric qualitatively agrees with the variance‐based metric and possibly identifies regions of nonlinear correlations. In application (2)–the climate ensemble–the information theory metric detects higher temperature intrinsic variability in the Arctic region compared to the variance metric illustrating that the former is robust in a skewed probability distribution (Arctic sea surface temperature) resulting from sharply nonlinear behavior (freezing point). In application (3)–coastal ensemble–variability is dominated by external forcing. Using different selective forcing ensembles, we quantify the sensitivity of the coastal model to different types of external forcing: variations in the river runoff and changes in wind product do not add information (i.e., variability) during summer. Information theory enables ranking how much each forcing type contributes across multiple variables.

 

The rotation of Earth breaks time-reversal and reflection symmetries in an opposite sense north and south of the equator, leading to a topological origin for certain atmospheric and oceanic equatorial waves. Away from the equator, the rotating shallow-water and stably stratified primitive equations exhibit Poincaré inertia–gravity waves that have nontrivial topology as evidenced by their strict superinertial time scale and a phase singularity in frequency–wavevector space. This nontrivial topology then predicts, via the principle of bulk-interface correspondence, the existence of two equatorial waves along the equatorial interface, the Kelvin and Yanai waves. To directly test the nontrivial topology of Poincaré-gravity waves in observations, we examine ERA5 data and study cross correlations between the wind velocity and geopotential height of the midlatitude stratosphere at the 50 hPa height. We find the predicted vortex and antivortex in the relative phase of the geopotential height and velocity at the high frequencies of the waves. By contrast, lower-frequency planetary waves are found to have trivial topology also as expected from theory. These results demonstrate a new way to understand stratospheric waves and provide a new qualitative tool to investigate waves in other components of the climate system.

 

Future sea-level change is characterized by both quantifiable and unquantifiable uncertainties. Effective communication of both types of uncertainty is a key challenge in translating sea-level science to inform long-term coastal planning. Scientific assessments play a key role in the translation process and have taken diverse approaches to communicating sea-level projection uncertainty. Here we review how past IPCC and regional assessments have presented sea-level projection uncertainty, how IPCC presentations have been interpreted by regional assessments and how regional assessments and policy guidance simplify projections for practical use. This information influenced the IPCC Sixth Assessment Report presentation of quantifiable and unquantifiable uncertainty, with the goal of preserving both elements as projections are adapted for regional application. 

Abstract Empirically generated indices are used to evaluate the skill of a global climate model in representing the monsoon intraseasonal oscillation (MISO). This work adapts the method of Suhas et al., an extended empirical orthogonal function (EEOF) analysis of daily rainfall data with the first orthogonal function indicating MISO strength and phase. This method is applied to observed rainfall and Community Earth System Model (CESM1.2) simulation results. Variants of the CESM1.2 including upper ocean parameterizations for Langmuir turbulence and submesoscale mixed layer eddy restratification are used together with the EEOF analysis to explore sensitivity of the MISO to global upper ocean process representations. The skill with which the model variants recreate the MISO strength and persistence is evaluated versus the observed MISO. While all model versions reproduce the northward rainfall propagation traditionally associated with the MISO, a version including both Langmuir turbulence and submesoscale restratification parameterizations provides the most accurate simulations of the time scale of MISO events. 

This work utilizes remotely sensed thermal data to understand how the release of thermal pollution from the Brayton Point Power Station (BPPS) affected the temperature behavior of Narragansett Bay. Building upon previous work with Landsat 5, a multi-satellite analysis is conducted that incorporates 582 scenes from Landsat 5, Landsat 7, and Landsat 8 over 1984–2021 to explain seasonal variability in effluent impacts, contrast data after the effluent ceased in 2011, identify patterns in temperature before and after effluent ceased using unsupervised learning, and track how recent warming trends compare to the BPPS impact. Stopping the thermal effluent corresponds to an immediate cooling of 0.26 ± 0.1°C in the surface temperature of Mt. Hope Bay with respect to the rest of Narragansett Bay with greater cooling of 0.62 ± 0.2°C found near Brayton Point; though, cooling since the period of maximal impact (1993–2000) totals 0.53 ± 0.2°C in Mt. Hope Bay and 1.04 ± 0.2°C at Brayton Point. During seasons with lower solar radiation (winter) and lower mean river input (autumn and late summer), the BPPS effluent impact is more prominent. The seasonal differences between the high impact and low impact periods indicate that river input played an important role in the heat balance when emissions were lower, but surface fluxes dominated when emissions were higher. Putting the BPPS effluent in context, Landsat data indicates that Narragansett Bay warmed 0.5–1.2°C over the period of measurement at an average rate of 0.23 ± 0.1°C/decade and that net warming in Mt. Hope Bay is near zero. This trend implies that Narragansett Bay has experienced climatic warming over the past four decades on the scale of the temperature anomaly in Mt. Hope Bay caused by the BBPS effluent.