Practical Stability of Impulsive Discrete Systems with Time Delays

The purpose of this paper is to investigate the practical stability problem for impulsive discrete systems with time delays. By using Lyapunov functions and the Razumikhin-type technique, some criteria which guarantee the practical stability and uniformly asymptotically practical stability of the addressed systems are provided. Finally, two examples are presented to illustrate the criteria

An atmospheric origin of the multi-decadal bipolar seesaw

A prominent feature of recent climatic change is the strong Arctic surface warming that is contemporaneous with broad cooling over much of Antarctica and the Southern Ocean. Longer global surface temperature observations suggest that this contrasting pole-to-pole change could be a manifestation of a multi-decadal interhemispheric or bipolar seesaw pattern, which is well correlated with the North Atlantic sea surface temperature variability, and thus generally hypothesized to originate from Atlantic meridional overturning circulation oscillations. Here, we show that there is an atmospheric origin for this seesaw pattern. The results indicate that the Southern Ocean surface cooling (warming) associated with the seesaw pattern is attributable to the strengthening (weakening) of the Southern Hemisphere westerlies, which can be traced to Northern Hemisphere and tropical tropospheric warming (cooling). Antarctic ozone depletion has been suggested to be an important driving force behind the recently observed increase in the Southern Hemisphere's summer westerly winds; our results imply that Northern Hemisphere and tropical warming may have played a triggering role at an stage earlier than the first detectable Antarctic ozone depletion, and enhanced Antarctic ozone depletion through decreasing the lower stratospheric temperature

Modeling the vertical structure of the ice shelf–ocean boundary current under supercooled condition with suspended frazil ice processes: A case study underneath the Amery Ice Shelf, East Antarctica

In contrast with the severe thinning of ice shelves along the coast of West Antarctica, large ice shelves (specifically, the Filchner–Ronne and Amery Ice Shelves) with deep grounding lines gained mass during the period 1994–2012. This positive mass budget is potentially associated with the marine ice production, which originates from the supercooled Ice Shelf Water plume carrying suspended frazil ice along the ice shelf base. In addition, the outflow of this supercooled plume from beneath the ice shelf arguably exerts a significant impact on the properties of Antarctic Bottom Water, as well as its production. However, knowledge of this buoyant and supercooled shear flow is still limited, let alone its structure that is generally assumed to be vertically uniform. In this study we extended the vertical one-dimensional model of ice shelf–ocean boundary current from Jenkins (2016) by incorporating a frazil ice module and a fairly sophisticated turbulence closure (i.e., k-ε model) with the effects of density stratification. On the basis of this extended model, the study reproduced the measured thermohaline properties of a perennially-prominent supercooled ice shelf–ocean​ boundary current underneath the Amery Ice Shelf in East Antarctica, and conducted extensive sensitivity runs to a wide range of factors, including advection of scalar quantities, far-field geostrophic currents, basal slope, and the distribution of frazil ice crystal size. Based on the simulation results, the following conclusions can be drawn: Firstly, it can be difficult to reasonably reproduce the vertical structure of the ice shelf–ocean boundary current using a constant eddy viscosity/diffusivity near the ice shelf base. Secondly, although there are no direct observations of the size of frazil ice crystals beneath the ice shelves, the size of the finest ice crystals that play an important role in controlling the ice shelf–ocean boundary current is strongly suggested. Lastly, but most importantly, the ice shelf–ocean boundary layer response to the vertical gradient of frazil ice concentration will significantly reduce the level of turbulence. Therefore, this study highlights the importance of the strong interaction between frazil ice formation and the hydrodynamics and thermodynamics of ice shelf–ocean boundary layer. This interaction must not only be included, but also be resolved at high resolutions in three-dimensional coupled ice shelf–ocean models applied to cold ice cavities, which will have a potential impact on the overall ice shelf mass balance and the Antarctic Bottom Water production

Rapid decline of total Antarctic sea ice extent during 2014–16 controlled by wind-driven sea ice drift

Between 2014 and 2016 the annual mean total extent of Antarctic sea ice decreased by a record, unprecedented amount of 1.6 3 106 km2, the largest in a record starting in the late 1970s. The mechanisms behind such a rapid decrease remain unknown. Using the outputs of a high-resolution, global ocean–sea ice model we show that the change was predominantly a result of record atmospheric low pressure systems over sectors of the Southern Ocean in 2016, with the associated winds inducing strong sea ice drift. Regions of large positive and negative sea ice extent anomaly were generated by both thermal and dynamic effects of the wind anomalies. Although the strong wind forcing also generated the warmest ocean surface state from April to December 2016, we show that enhanced northward sea ice drift and hence increased melting at lower latitudes driven by strong winds made the dominant contribution to the large decrease in total Antarctic sea ice extent between 2014 and 2016

On the determination and simulation of seawater freezing point temperature under high pressure

At present, it is believed that the freezing point temperature of seawater is a function of salinity and pressure, and the freezing point is a key parameter in a coupled air-sea-ice system. Generally, empirical formulas or methods are used to calculate the freezing point of seawater. Especially in high-pressure situations, e.g., under a thick ice sheet or ice shelf, the pressure term must be taken into account in the determination of seawater freezing point temperature. This study summarized various methods that have been used to calculate seawater freezing point with high pressure. The methods that were employed in two ocean-ice models were also assessed. We identified the disadvantages of these methods used in these two models and addressed the corresponding uncertainties of the freezing point temperature formulas. This study provides useful information on the calculation of the freezing point temperature in numerical modeling and indicates a need to investigate the sensitivity of numerical simulations to the uncertainties in the freezing point temperature in future