Research progress on firn densification models in polar ice sheets
Glaciers are transformed from snowflakes formed by the condensation of atmospheric water vapor at low temperatures. In general,the transformation of snowflakes to glaciers contains three processes. To begin with,the snowflakes falling on the surface of glaciers are automatically rounded and transformed into firn be-cause a system is more stable when its surface free energy is lower. The subsequent step is firn densification,a lengthy and challenging process that turns firn into glacier ice. During firn densification,firn density increases with depth and time due largely to overburden stress from the accumulation of new snow. Finally,glacier ice flows and progressively converts into glaciers under the force of gravity. Firn densification is a highly complicat-ed process since several physical mechanisms operate simultaneously during densification and dominant mecha-nisms differ at different stages. Understanding the evolution of density and the physics of firn densification is es-sential for several applications of glaciology. A firn densification model that can simulate the density evolution of firn is crucial for assessing glacier mass balance accurately via the satellite altimetry method. In this method,the differencing of digital elevation models provides a change in glacier volume,which needs to be converted to a mass change by a density model or assumption. The paleoclimate reconstruction of the ice core requires calcu-lating the age difference between the ice and the air trapped in it. A firn densification model is necessary to deter-mine the age of the ice when the bubbles are close-off,which can be coupled to a firn-air model to calculate the age difference. This paper comprehensively analyzes the research methodology and the latest progress on firn densification in polar ice sheets. Numerous firn densification models have been proposed in recent years. These models are categorized as either empirical models (including semi-empirical models) or physical models. Empir-ical models are often based upon a steady-state assumption. They are formulated as a function of temperature,accumulation rate (which serves as a proxy for stress),and several tuning parameters. The temperature sensitivi-ty has been improved by taking the effects of seasonal and interannual temperature variations into account. More recently,the impact of surface meltwater on firn densification rates,including meltwater percolation,retention,and refreezing,has been added into firn densification models. Physical models are built upon physical principles by analyzing the change in grain microstructure and its underlying physical mechanism during firn densification. These models were formulated by microscopic parameters (for example,grain radius,bond radius,and viscosi-ty). Physical models are currently scarce since the physics of firn densification is not fully understood,and the data needed to develop a purely physical model are still lacking. Up to now,the snow-firn transition is based on the theory describing grain-boundary sliding;the firn-ice transition is based on the theory explaining the pressure sintering of spherical powders. Overall,the study of firn densification in polar ice sheets has made great strides over the past few decades. On a macroscopic scale,the growth and deformation of grains are mainly affected by their microstructure. Both empirical and physical models are unsatisfactory because previous studies on firn den-sification have not yet fully clarified the microstructure of firn and its connection to the macroscopic process. For the empirical models,the theory of wet firn densification is still incomplete. And the applicability of empirical models is limited due to the neglect of the specific physical mechanisms. In addition,it may fail to generalize the steady-state assumption directly to transient scenarios. The physical models employed today are mainly based on idealized assumptions,which may be speculative and unreliable because the physics of firn densifica-tion is still uncertain.
Greenland ice sheetAntarctic ice sheetfirn densificationfirn density evolution