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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2018

Decadal Evolution of the Surface Energy Budget During the Fast Warming and Global Warming Hiatus Periods in the ERA-Interim

The global-mean surface temperature has experienced a rapid warming from the 1980s to early-2000s but a muted warming since, referred to as the global warming hiatus in the literature. Decadal changes in deep ocean heat uptake are thought to primarily account for the rapid warming and subsequent slowdown. Here, we examine the role of ocean heat uptake in establishing the fast warming and warming hiatus periods in the ERA-Interim through a decomposition of the global-mean surface energy budget. We find the increase of carbon dioxide alone yields a nearly steady increase of the downward longwave radiation at the surface from the 1980s to the present, but neither accounts for the fast warming nor warming hiatus periods. During the global warming hiatus period, the transfer of latent heat energy from the ocean to atmosphere increases and the total downward radiative energy flux to the surface decreases due to a reduction of solar absorption caused primarily by an increase of clouds. The reduction of radiative energy into the ocean and the surface latent heat flux increase cause the ocean heat uptake to decrease and thus contribute to the slowdown of the global-mean surface warming. Our analysis also finds that in addition to a reduction of deep ocean heat uptake, the fast warming period is also driven by enhanced solar absorption due predominantly to a decrease of clouds and by enhanced longwave absorption mainly attributed to the air temperature feedback.

Hu, Xiaoming↗
NASA NTRS2022

Responses of Compound Daytime and Nighttime Warm-Dry and Warm-H Events to Individual Anthropogenic Forcings

Daytime heat is often associated with reduced soil moisture and cloud cover, while nighttime heat is connected to high humidity and increased cloud cover. Due to these differing mechanisms, compound daytime and nighttime heat events may respond differently to major anthropogenic forcings (greenhouse gases, anthropogenic aerosols, land-use and land-cover change). Here, we use GISS ModelE2.1-G historical single-forcing runs from 1955 to 2014 to examine how individual anthropogenic forcings affect compound heat events—specifically warm daytime and nighttime temperatures compounded with dry precipitation or high humidity conditions. We show that greenhouse gases alone amplify the natural frequency of warm-dry events by 1.5–5 times and warm-humid events by 2–9 times in tropical and extratropical latitudes. Conversely, aerosols and land-use/land-cover change reduce the frequency of these events, resulting in more modest increases and in some regions, declines, in the historical 'all-forcings' scenario. Individually, aerosol effects are stronger and more widespread compared to land-use, oftentimes reducing the natural frequency of these events by 60%–100%. The responses of these compound events are primarily driven by changes in daytime and nighttime temperatures through large-scale warming via greenhouse gases and cooling from aerosols and land-use/land-cover change. However, changes in warm-dry events are amplified in regions with concurrent precipitation declines (e.g. Central America, Mediterranean regions) and warm-humid events are amplified by global concurrent humidity increases. Additionally, we find differences between daytime and nighttime compound responses in the historical experiment that can be traced back to the individual forcings. In particular, aerosols produce a greater cooling effect on daytime relative to nighttime temperatures, which notably results in a historical reduction of Northern Hemisphere daytime warm-dry events relative to natural conditions. Our analysis provides a more comprehensive understanding of the significant impacts of different anthropogenic climate forcings on daytime and nighttime warm-dry and warm-humid events, informing future risk and impact assessments.

Anthropogenic forcings↗
NASA NTRS1985

Discrimination of a major stratospheric warming event in February-March 1984 from earlier minor warmings

As part of its responsibility for stratospheric monitoring, the Climate Analysis Center derives time trends of various dynamic parameters from NMC stratospheric analyses. Selected figures from this stratospheric monitoring data base are published in Climate Diagnostics Bulletin in March and October, after each hemispheric winter. During the Northern Hemisphere winter of December 1983-February 1984 several warming events may be seen in the plot of 60 deg. N zonal mean temperatures for 10 mb. Minor warmings may be noted in early December, late December, mid January and early February. A major warming with the 60 deg. N zonal mean temperatures reaching -40C is observed in late February, associated with a circulation reversal. In all of the minor warming episodes, there is a polarward movement of the Aleutian anticyclone; however, at 10 mb the North Pole remains in the cyclonic circulation of the stratospheric vortex which is not displaced far from its usual position. In the case of the later February major warming, the 10 mb circulation pattern over the North Pole is anticyclonic, and the cyclonic circulation has moved to the south and east with a considerable elongation. Cross sections of heat transport and momentum transport are not dramatically different for the minor and major warming episodes.

Johnson, K. W.↗
NASA NTRS1981

On the warming of the polar troposphere during the stratospheric warming of January 1977

In January 1977, a warming of the polar troposphere occurred following a major stratospheric warming. The temperature increase in the polar troposphere is found to be larger below 400 mb than in the upper troposphere. Analysis of the heat budget of the polar troposphere shows that the eddy heat flux convergence is the major factor responsible for the tropospheric warming.

Hansen, A. R.↗
NASA NTRS2021

The Influence of Direct Radiative Forcing Versus Indirect Sea Surface Temperature Warming on Southern Hemisphere Subtropical Anticyclones Under Global Warming

Southern hemisphere subtropical anticyclones are projected to change in a warmer climate during both austral summer and winter. A recent study of CMIP 5 & 6 projections found a combination of local diabatic heating changes and static-stability-induced changes in baroclinic eddy growth as the dominant drivers. Yet the underlying mechanisms forcing these changes still remain uninvestigated. This study aims to enhance our mechanistic understanding of what drives these Southern Hemisphere anticyclones changes during both seasons. Using an AGCM, we decompose the response to CO2-induced warming into two components: (1) the fast atmospheric response to direct CO2 radiative forcing, and (2) the slow atmospheric response due to indirect sea surface temperature warming. Additionally, we isolate the influence of tropical diabatic heating with AGCM added heating experiments. As a complement to our numerical AGCM experiments, we analyze the Atmospheric and Cloud Feedback Model Intercomparison Project experiments. Results from sensitivity experiments show that slow subtropical sea surface temperature warming primarily forces the projected changes in subtropical anticyclones through baroclinicity change. Fast CO2 atmospheric radiative forcing on the other hand plays a secondary role, with the most notable exception being the South Atlantic subtropical anticyclone in austral winter, where it opposes the forcing by sea surface temperature changes resulting in a muted net response. Lastly, we find that tropical diabatic heating changes only significantly influence Southern Hemisphere subtropical anticyclone changes through tropospheric wind shear changes during austral winter.

Subtropical anticyclone↗
NASA NTRS1978

Numerical simulation of warm fog and its application to warm fog prediction and modification

The considered theoretical model describes the evolution of potential temperature, water vapor content, liquid water content, and horizontal and vertical winds as determined by the processes of vertical turbulent transfer and horizontal advection for momentum, energy, and moisture, as well as radiation cooling, growth of water droplets based on microphysical processes, and drop sedimentation. The mathematical model is two-dimensional in the X-Z plane. The diffusivity coefficient is the same for liquid water droplets as for vapor. The fundamental equations governing the macrophysical processes of the evolution of wind components, water vapor content, liquid water content, and potential temperature under the influences of vertical turbulent diffusion transfer, turbulent momentum transfer, and turbulent energy transfer are expressed by three sets of conservation equations.

Hung, R. J.↗
NASA NTRS1980

Description of the warm core turbine facility and the warm annular cascade facility recently installed at NASA Lewis Research Center

The two new facilities have been installed and operated at their design or rated conditions. The important feature of both of these facilities is that the ratio of turbine inlet temperature to coolant temperature encountered in high temperature engines can be duplicated at moderate turbine inlet temperature. Included in the discussion are the limits of the facilities with regard to maximum temperature, maximum pressure, maximum mass flow rate, turbine size, and dynamometer torque-speed characteristics.

Whitney, W. J.↗
NASA NTRS2024

Aera-Mip: Emission Pathways, Remaining Budgets, and Carbon Cycle Dynamics Compatible With 1.5 and 2 °C Global Warming Stabilization

While international climate policies now focus on limiting global warming to well below 2 °C or pursuing a 1.5 °C level of global warming, the climate modelling community has not provided an experimental design in which all Earth system models (ESMs) converge and stabilize at the same prescribed global warming levels. This gap hampers accurate estimations based on comprehensive ESMs of the carbon emission pathways and budgets needed to meet such agreed warming levels and of the associated climate impacts under temperature stabilization. Here, we apply the Adaptive Emission Reduction Approach (AERA) with ESMs to provide such simulations in which all models converge at 1.5 and 2.0 °C warming levels by adjusting their emissions over time. These emission-driven simulations provide a wide range of emission pathways and resulting atmospheric CO 2 projections for a given warming level, uncovering uncertainty ranges that were previously missing in the traditional Coupled Model Intercomparison Project (CMIP) scenarios with prescribed greenhouse gas concentration pathways. Meeting the 1.5 °C warming level requires a 40 % (full model range: 7 % to 76 %) reduction in multi-model mean CO 2 -forcing-equivalent (CO 2 -fe) emissions from 2025 to 2030, a 98 % (57 % to 127 %) reduction from 2025 to 2050, and a stabilization at 1.0 (−1.7 to 2.9) PgC yr−1 from 2100 onward after the 1.5 °C global warming level is reached. Meeting the 2.0 °C warming level requires a 47 % (8 % to 92 %) reduction in multi-model mean CO 2 -fe emissions until 2050 and a stabilization at 1.7 (−1.5 to 2.7) PgC yr−1 from 2100 onward. The on-average positive emissions under stabilized global temperatures are the result of a decreasing transient climate response to cumulative CO 2 -fe emissions over time under stabilized global warming. This evolution is consistent with a slightly negative zero emissions commitment – initially assumed to be zero – and leads to an increase in the post-2025 CO 2 -fe emission budget by a factor of 2.2 (−0.8 to 6.9) by 2150 for the 1.5 °C warming level and a factor of 1.4 (0.9 to 2.4) for the 2.0 °C warming level compared to its first estimate in 2025. The median CO 2 -only carbon budget by 2150, relative to 2020, is 800 GtCO 2 for the 1.5 °C warming level and 2250 GtCO 2 for the 2.0 °C warming level. These median values exceed the median IPCC AR6 estimates by 60 % for the 1.5 °C warming level and 67 % for 2.0 °C. Some of the differences may be explained by the choice of the mitigation scenario for non-CO 2 radiative agents. Our simulations highlight shifts in carbon uptake dynamics under stabilized temperature, such as a cessation of the carbon sinks in the North Atlantic and in tropical forests. On the other hand, the Southern Ocean remains a carbon sink centuries after temperatures stabilize. Overall, this new type of warming-level-based emission-driven simulation offers a more coherent assessment across climate models and opens up a wide range of possibilities for studying both the carbon cycle and climate impacts, such as extreme events, under climate stabilization.

Adaptive Emission Reduction Approach↗
NASA NTRS1999

Simulation of the December 1998 Stratospheric Major Warming

Prior to 1991, major warmings (defined by increasing zonal mean temperatures and zonal mean easterly winds from 60degN to the pole at 10 hPa) typically occurred approximately once every two Arctic winters; a major warming in mid-Dec. 1998 was the first since Feb. 1991. The Dec. 1998 warming was also the second earliest on record. The earliest, and the only other major warming on record before the end of Dec. was in early Dec 1987; prior to that, the earliest was in late Dec./early Jan. 1984-85. The 1984-85 and 1987 warmings resulted in the warmest and weakest lower stratospheric polar vortices in the 20 years before 1998-99. Fig. 1 compares temperatures and vortex strength in 1998-99 with those in the previous 20 years, using the US National Center for Environmental Prediction (NCEP) record; 1987-88 and 1984-85 are also highlighted. The Dec. 1998 warming had a more pronounced effect on mid-stratospheric temperatures than the Dec. 1987 warming (Fig. 1a), although smaller than that of warmings later in winter (e.g., 1984-85). 10-hPa temperatures fell well below average again in late Jan. 1999 and remained unusually low until an early final warming began in late Feb. 840 K PV gradients (Fig. 1c) set a record minimum in Jan. 1999, but were near average in Feb before the final warming. The effect of the Dec. 1998 warming on lower stratospheric temperatures was comparable to that of other major warmings; there was a brief period of record-high minimum 46-hPa temperatures in early Jan 1999 (Fig. 1b), and temperatures then fell to near average for a short period in mid-Feb. Lower stratospheric PV gradients were the weakest on record during the 1998-99 winter (Fig. 1d). The evolution of the vortex and minimum temperatures during 1998-99 was remarkably similar to that during 1987-88, the only previous year when a major warming was observed before the end of Dec.

Manney, G. L.↗
NASA NTRS1987

Simulated sudden stratospheric warming - Synoptic evolution

An analysis is presented of a sudden stratospheric warming event which occurred spontaneously during a general circulation model simulation of the global atmospheric circulation. Two separate warming pulses exhibit the same dynamical evolution with a 'cycle' of about two weeks. Two distinct phases of the warming cycle are apparent: (1) the generation of an intense localized warm cell in conjunction with significant adiabatic heating associated with cross-isobar flow which has been induced by vertically propagating long wave disturbances; and (2) the northward transport of that warm cell via advection by the essentially geostrophic windfield corresponding to an intense, offset polar cyclone, in conjunction with a strong Aleutian anticyclone. During the first warming pulse in January, a moderate Aleutian anticyclone was in place prior to the warming cycle and was intensified by interaction with an eastward traveling anticyclone induced by the differential advection of the warm cell. The second warming pulse occurred in early February with a strong Aleutian anticyclone already established. In contrast to the January event, the warming in February culminated with reversal of the zonal westerlies to easterlies over a significant depth of the stratosphere.

Blackshear, W. T.↗
NASA NTRS2001

Warm-Core Intensification Through Horizontal Eddy Heat Transports into the Eye

A simulation of Hurricane Bob (1991) using the PSU/NCAR MM5 mesoscale model with a finest mesh spacing of 1.3 km is used to diagnose the heat budget of the hurricane. Heat budget terms, including latent and radiative heating, boundary layer forcing, and advection terms were output directly from the model for a 6-h period with 2-min frequency. Previous studies of warm core formation have emphasized the warming associated with gentle subsidence within the eye. The simulation of Hurricane Bob confirms subsidence warming as a major factor for eye warming, but also shows a significant contribution from horizontal advective terms. When averaged over the area of the eye, subsidence is found to strongly warm the mid-troposphere (2-9 km) while horizontal advection warms the mid to upper troposphere (5-13 km) with about equal magnitude. Partitioning of the horizontal advective terms into azimuthal mean and eddy components shows that the mean radial circulation does not, as expected, generally contribute to this warming, but that it is produced almost entirely by the horizontal eddy transport of heat into the eye. A further breakdown of the eddy components into azimuthal wave numbers 1, 2, and higher indicates that the warming is dominated by wave number 1 asymmetries, with smaller coming from higher wave numbers. Warming by horizontal eddy transport is consistent with idealized modeling of vortex Rossby waves and work is in progress to identify and clarify the role of vortex Rossby waves in warm-core intensification in both the full-physics model and idealized models.

Braun, Scott A.↗
NASA NTRS2001

Warm-Core Intensification of a Hurricane Through Horizontal Eddy Heat Transports Inside the Eye

A simulation of Hurricane Bob (1991) using the PSU/NCAR MM5 mesoscale model with a finest mesh spacing of 1.3 km is used to diagnose the heat budget of the hurricane. Heat budget terms, including latent and radiative heating, boundary layer forcing, and advection terms were output directly from the model for a 6-h period with 2-min frequency. Previous studies of warm core formation have emphasized the warming associated with gentle subsidence within the eye. The simulation of Hurricane Bob also identifies subsidence warming as a major factor for eye warming, but also shows a significant contribution from horizontal advective terms. When averaged over the area of the eye, excluding the eyewall (at least in an azimuthal mean sense), subsidence is found to strongly warm the mid-troposphere (2-9 km) while horizontal advection warms the mid to upper troposphere (5-13 km) with about equal magnitude. Partitioning of the horizontal advective terms into azimuthal mean and eddy components shows that the mean radial circulation cannot, as expected, generally contribute to this warming, but that it is produced almost entirely by the horizontal eddy transport of heat into the eye. A further breakdown of the eddy components into azimuthal wave numbers 1, 2, and higher indicates that the warming is dominated by wave number 1 asymmetries, with smaller contributions coming from higher wave numbers. Warming by horizontal eddy transport is consistent with idealized modeling of vortex Rossby waves and work is in progress to identify and clarify the role of vortex Rossby waves in warm-core intensification in both the full-physics model and idealized models.

Braun, Scott A.↗
NASA NTRS2005

Simulations of Dynamics and Transport during the September 2002 Antarctic Major Warming

A mechanistic model simulation initialized on 14 September 2002, forced by 100-hPa geopotential heights from Met Office analyses, reproduced the dynamical features of the 2002 Antarctic major warming. The vortex split on approx.25 September; recovery after the warming, westward and equatorward tilting vortices, and strong baroclinic zones in temperature associated with a dipole pattern of upward and downward vertical velocities were all captured in the simulation. Model results and analyses show a pattern of strong upward wave propagation throughout the warming, with zonal wind deceleration throughout the stratosphere at high latitudes before the vortex split, continuing in the middle and upper stratosphere and spreading to lower latitudes after the split. Three-dimensional Eliassen-Palm fluxes show the largest upward and poleward wave propagation in the 0(deg)-90(deg)E sector prior to the vortex split (coincident with the location of strongest cyclogenesis at the model's lower boundary), with an additional region of strong upward propagation developing near 180(deg)-270(deg)E. These characteristics are similar to those of Arctic wave-2 major warmings, except that during this warming, the vortex did not split below approx.600 K. The effects of poleward transport and mixing dominate modeled trace gas evolution through most of the mid- to high-latitude stratosphere, with a core region in the lower-stratospheric vortex where enhanced descent dominates and the vortex remains isolated. Strongly tilted vortices led to low-latitude air overlying vortex air, resulting in highly unusual trace gas profiles. Simulations driven with several meteorological datasets reproduced the major warming, but in others, stronger latitudinal gradients at high latitudes at the model boundary resulted in simulations without a complete vortex split in the midstratosphere. Numerous tests indicate very high sensitivity to the boundary fields, especially the wave-2 amplitude. Major warmings occurred for initial fields with stronger winds and larger vortices, but not smaller vortices, consistent with the initiation of wind-deceleration by upward-propagating waves near the poleward edge of the region where wave 2 can propagate above the jet core. Thus, given the observed 100-hPa boundary forcing, stratospheric preconditioning is not needed to reproduce a major warming similar to that observed. The anomalously strong forcing in the lower stratosphere can be viewed as the primary direct cause of the major warming.

winds↗
NASA NTRS2021

Elevation Dependent Warming in the Eastern Siberian Arctic

There is evidence for elevation-dependent warming (EDW) in many mountainous regions, including the Alps, Rockies, and Tibetan Plateau, all of which are in mid-latitudes. Most studies finding evidence of EDW indicate that both recent decadal and future projected warming rates are greater at higher elevations. In this study, we examine the roles of Arctic amplification and elevation on future warming rates in winter and summer in eastern Siberia (50-70°N; 80-180°E). This region includes four major river basins that flow into the Arctic Ocean (the Yenisei, Lena, Indigirka, and Kolyma) and intersects with mountain ranges in northern Mongolia and eastern Siberia. We analyse projected 21st century temperature projections using a six-member ensemble of the National Center for Atmospheric Research (NCAR) Community Climate System Model (CCSM4) with a radiative forcing of 8.5 W m-2. Projected warming rates in winter for the 21st century are dominated by Arctic amplification, which leads to significantly larger warming rates at higher latitudes, with latitudinal gradients of about 0.16°C per degree latitude. In summer, the latitudinal gradient is near zero (0.02°C per degree of latitude). Within specific latitude bands, we also find EDW. However, unlike most mid-latitude locations where warming rates are greater at higher elevations, we find that future warming rates are smaller at higher elevations for this high-latitude region, particularly during winter, with statistically significant rates varying between -0.70 and -2.46 °C/km for different 5° latitude bands. The decrease in warming rates with elevation in winter at the highest latitudes is primarily attributed to strong inversions and changes in the lapse rate as free-air temperatures warm at slower rates than surface temperatures. In summer, the elevation dependence is much weaker than in winter but still statistically significant and negative in all but the most northern latitude band with values ranging between -0.10 and -0.56 °C/km.

elevation-dependent warming (EDW)↗
NASA NTRSDate not supplied

Warming Reduces the Efficacy of Wet Conditions to Moderate Extreme Heat and Atmospheric Aridity Across the Central Plains

In the literature, dry land surface conditions possess a well-established association with extreme heat and high atmospheric aridity, especially in regions that experience strong land-atmosphere feedbacks. However, few studies have examined whether global warming will impact the ability of wet conditions to constrain high temperatures and atmospheric aridity occurrences. Here we investigate how wet conditions, which we define using precipitation and soil moisture, constrain high temperature and high vapor pressure deficit during the warm season over the Central Plains in North America at different global warming levels (0-3 degrees K). Using a CMIP6 multi-model ensemble, we show that absolute changes in the maximum temperature distribution outweigh the historical cooling effect of high precipitation or soil moisture conditions, reducing the probability of non-extreme maximum temperatures under global warming. Strikingly, the conditional likelihood of non-extreme maximum temperatures falls from 97-98% at baseline conditions to 50-58% at 1 degree of global warming. Once 2 degrees of warming is reached, there is very little probability of constraining extreme maximum temperatures. On the other hand, high precipitation and high soil moisture are able to better retain the ability to constrain concurrent high vapor pressure deficit conditions – moving from 99% at baseline conditions to 81-91% at 1 degree of warming and 26-42% at 2 degrees of warming. With our results, we find that the extent of this retention is dependent on how individual models represent relative changes in the VPD distribution as temperatures warm. Overall, our results highlight the growing vulnerability of the Central North American region to warmer temperatures and drier atmospheric conditions, even during periods of high precipitation and soil moisture.

Extreme heat↗
NASA NTRS1975

A comparison of observed and simulated properties of sudden stratospheric warmings

Review of observational data and dynamical numerical simulations of stratospheric warmings. Classes of warmings, major and minor (major if poleward movement of planetary-scale thermal systems entails reversal of polar circulation at 10 mb or below), trajectories of warm cells, vertical and horizontal scale of warm-air systems, the time-scale of warming, initial zonal flow conditions prior to a warming, circulation reversals, and details of the energy budget before and after a warming are discussed. The 1963 and 1973 types of warmings are contrasted: the strong baroclinic conversion of eddy potential to eddy kinetic energy was not repeated in the latter, but both events were preceded by very large fluxes from the troposphere. Numerical model simulations by various authors are compared and evaluated.

Quiroz, R. S.↗
NASA NTRS1981

Energetics of a sudden stratospheric warming simulated with a three-dimensional, spectral, quasi-geostrophic model

The energetics of a three dimensional, quasi-geostrophic simulation of a sudden stratospheric warming which developed spontaneously during an annual cycle simulation are described. Daily values of the stratospheric temperatures, zonal winds, heating rates, energies, and energy conversions are discussed and compared with those for observed warmings. It is shown that, like observed warmings, the simulated warming was preceded by an increased vertical flux of eddy kinetic energy from the troposphere and the polar heating resulted because of the strong convergence of the horizontal, eddy heat flux which was only partially balanced by adiabatic and diabatic cooling. There is a significant similarity between the energetics of the simulated and observed warmings. In addition, the warming was spontaneous and the model did not develop a major warming in each winter of the simulation. These facts suggest that this model may be useful for studying not only the warming process but also the conditions that favor its development.

Haggard, K. V.↗
NASA NTRS1993

The interaction of radiative and dynamical processes during a simulated sudden stratospheric warming

An analysis of a spontaneous sudden stratospheric warming that occurred during a 2-year integration of the Langley Research Center (LaRC) Atmospheric Simulation Model is presented. The simulated warming resembles observed 'wave 1' warmings in the Northern Hemisphere stratosphere and provides an opportunity to investigate the radiative and dynamical processes occurring during the warming event. Isentropic analysis of potential vorticity sources and sinks indicates that dynamically induced departures from radiative equilibrium play an important role in the warming event. Enhanced radiative cooling associated with a series of upper stratospheric warm pools leads to radiative dampening within the polar vortex. Within the 'surf zone' large-scale radiative cooling leads to diabatic advection of high potential vorticity air from aloft. Lagrangian area diagnostics of the simulated warming agree well with Limb Infrared Monitor of the Stratosphere (LIMS) analyses. Dynamical mixing is shown to account for the majority of the decrease in the size of the polar vortex during the simulated warming. An investigation of the nonlinear deformation of material lines that are initially coincident with diagnosed potential vorticity isopleths is conducted to clarify the relationship between the Lagrangian area diagnostics and potential vorticity advection during wave breaking events.

Pierce, R. B.↗