Two ice core boreholes of 143.18 m and 447.73 m (bedrock) were drilled during the 2009–2010 austral summer on the Bruce Plateau at a location named LARISSA Site Beta (66°02' S, 64°04' W, 1975.5 m a.s.l.). Both boreholes were logged with thermistors shortly after drilling. The shallow borehole was instrumented for 4 months with a series of resistance thermometers with satellite uplink. Surface temperature proxy data derived from an inversion of the borehole temperature profiles are compared to available multi-decadal records from weather stations and ice cores located along a latitudinal transect of the Antarctic Peninsula to West Antarctica. The LARISSA Site Beta profiles show temperatures decreasing from the surface downward through the upper third of the ice, and warming thereafter to the bed. The average temperature for the most recent year is −14.78°C (measured at 15 m depth, abbreviated T₁₅). A minimum temperature of −15.8°C is measured at 173 m depth, and basal temperature is estimated to be −10.2°C. Current mean annual temperature and the gradient in the lower part of the measured temperature profile have a best fit with an accumulation rate of 1.9×10³ kg m⁻² a⁻¹ and basal heat flux (q) of 88 mW m⁻², if steady-state conditions are assumed. However, the mid-level temperature variations show that recent temperature has varied significantly. Reconstructed surface temperatures (T_s=T₁₅) over the last 200 yr are derived by an inversion technique (Tikhonov and Samarskii, 1990). From this, we find that cold temperatures (minimum T_s=−16.2°C) prevailed from ~1920 to ~1940, followed by a gradual rise of temperature to −14.2°C around 1995, then cooling over the following decade and warming in the last few years. The coldest period was preceded by a relatively warm 19th century at T₁₅≥−15°C. To facilitate regional comparisons of the surface temperature history, we use our T₁₅ data and nearby weather station records to refine estimates of lapse rates (altitudinal, adjusted for latitude: Γ_a(l)). Good temporal and spatial consistency of Γ_a(l) over the last 35 yr are observed, implying that the climate trends observed here are regional and consistent over a broad altitude range.

Seasonal temperature variations occur in the glacier layer about 15–20 m below the surface, while at greater depths the glacier temperature depends on the long-term surface conditions. It is generally accepted that for glaciers without surface melting the temperature at 10 m depth (T₁₀) is close to the mean annual air temperature at standard screen level (T_a), i.e. T₁₀ =T_a. We found that this relationship is not valid for T_a above –17˚C and below –55˚C. The goal of our investigation is to find a better temperature transfer function (TTF) between T_a and temperature at the boundary of the active layer in accumulation areas of polar and tropical glaciers. Low-precision T₁₀ temperatures from boreholes, obtained at 41 sites, are compared with air temperatures (T_a) measured in the vicinity of these sites for at least a 1 year period. We determine that when T_a falls into the temperature range –60 to –7˚C, empirical values can be approximated as T₁₀ = 1:2T_a + 6:7. Analysis of these data suggests that high T₁₀ occurs in the areas of the glacier that collect meltwater.

Two modifications with variable coefficients of the well-known SEIR model for epidemic development in the application to the modeling of the infection curves of COVID-19 are considered. The data for these models are information on the number of infections each day obtained from the Johns Hopkins Coronavirus Resource Center database. In our paper, we propose special methods based on Tikhonov regularization for models’ identification on the class of piecewise constant coefficients. In contrast to the model with constant coefficients, which cannot always accurately describe some of infection curves, the first model is able to approximate them for different countries with an accuracy of 2–8%. The second model considered in the article takes into account external sources of infection in the form of an inhomogeneous term in one of the model equations and is able to approximate the data with a slightly better accuracy of 2–4%. For the second model, we also consider the possibility of using other input data, namely the number of infected people per day. Such data are used to model infection curves for several waves of the COVID-19 epidemic, including part of the Omicron wave. Numerical experiments carried out for a number of countries show that the waves of external sources of infection found are ahead of the wave of infection by 10 or more days. At the same time, other piecewise constant coefficients of the model change relatively slowly. These models can be applied fairly reliably to approximate many waves of infection curves with high precision and can be used to identify external and hidden sources of infection. This is the advantage of our models.