Impact of Laptev Sea flaw polynyas on the atmospheric boundary layer and ice production using idealized mesoscale simulations

The interaction between polynyas and the atmospheric boundary layer is examined in the Laptev Sea using the regional, non-hydrostatic Consortium for Small-scale Modelling (COSMO) atmosphere model. A thermodynamic sea-ice model is used to consider the response of sea-ice surface temperature to idealized atmospheric forcing. The idealized regimes represent atmospheric conditions that are typical for the Laptev Sea region. Cold wintertime conditions are investigated with sea-ice–ocean temperature differences of up to 40 K. The Laptev Sea flaw polynyas strongly modify the atmospheric boundary layer. Convectively mixed layers reach heights of up to 1200 m above the polynyas with temperature anomalies of more than 5 K. Horizontal transport of heat expands to areas more than 500 km downstream of the polynyas. Strong wind regimes lead to a more shallow mixed layer with strong near-surface modifications, while weaker wind regimes show a deeper, well-mixed convective boundary layer. Shallow mesoscale circulations occur in the vicinity of ice-free and thin-ice covered polynyas. They are forced by large turbulent and radiative heat fluxes from the surface of up to 789 W m−2, strong low-level thermally induced convergence and cold air flow from the orographic structure of the Taimyr Peninsula in the western Laptev Sea region. Based on the surface energy balance we derive potential sea-ice production rates between 8 and 25 cm d−1. These production rates are mainly determined by whether the polynyas are ice-free or covered by thin ice and by the wind strength.

Shadow lines in the arithmetic of elliptic curves

Let E/Q be an elliptic curve and p a rational prime of good ordinary reduction. For every imaginary quadratic field K/Q satisfying the Heegner hypothesis for E we have a corresponding line in E(K)\otimes Q_p, known as a shadow line. When E/Q has analytic rank 2 and E/K has analytic rank 3, shadow lines are expected to lie in E(Q)\otimes Qp. If, in addition, p splits in K/Q, then shadow lines can be determined using the anticyclotomic p-adic height pairing. We develop an algorithm to compute anticyclotomic p-adic heights which we then use to provide an algorithm to compute shadow lines. We conclude by illustrating these algorithms in a collection of examples.