Billiards are idealizations for systems where particles or waves are confined to cavities, or to other homogeneous regions. In billiard systems a point particle moves freely except for specular reflections from rigid walls. However, billiard walls are not always completely reflective and measurements inside can also open the billiard. Since boundary openings have been studied extensively in the literature, we rather model leakages inside the billiard. In particular, we investigate the classical dynamics of a leakage for a continuous family of billiard systems, that is, the stadium-lemon-billiard family. With a single parameter the geometry of the billiard can be tuned from stadium (being fully hyperbolic) over circle (integrable) to the lemon-shaped billiard (mixed chaotic). For the stadium billiard we found an algebraically decaying mean escape time with the linear size of the leakage n(esc) approximately epsilon-1 together with an exponential decay of the survival probability distribution. The finding is nearly independent of the position and size of the leakage, as long as the leakage is much smaller than the system size, and it is in good agreement with a stochastic map approximation of the dynamics. Due to the mixed phase space for lemon billiards, the mean escape time depends both on the position and geometry of the leakage. For systems where quasiregular motion dominates, we found a linear dependence of the mean escape time, n(esc) approximately 1-epsilon, which we refer to as flooding law. Our findings are helpful in understanding dynamics of leaking Hamiltonian systems.

Abstract. In this study, we analyse the climatic impacts on the grape harvest date (GHD) in Burgundy (France) on interannual and decadal time scales. We affirm that the GHD is mainly influenced by the local April-to-August temperature (AAT) and provide the spatial expansion of this relationship. The spatial correlation pattern yields similar results for the instrumental and pre-instrumental period, indicating the consistency of the pre-instrumental field data with the instrumental GHD-spring/summer relationship. We find a previously undocumented second climate impact on the GHD. The winter temperature is significantly correlated with the GHD on decadal-to-multidecadal time scales and affects the GHD independently of the AAT. A multiple linear regression model, with AAT and decadal winter temperature as predictors, was found to be the best model to describe the GHD time series for the instrumental period. Stability tests of the correlations over time yield that both impacts on the GHD, AAT and decadal winter temperature, strengthen during the instrumental period. Using partial correlation analysis, we demonstrate that this is partly caused by a change in the winter-spring/summer temperature relationship. Summarising, the GHD is well suited to reconstruct interannual variations of the spring/summer temperature over large parts of Europe, even if the changing winter-spring/summer relation might affect the reconstruction in a second order. For decadal time scales, the December-to-August temperature shows the strongest relationship to the GHD and, therefore, proposes that the GHD can be used for European temperature reconstructions beyond the spring/summer season. Finally, we argue that our findings regarding the changed Correspondence to: M. Krieger (kriegerm@uni-bremen.de) winter-spring/summer relation are relevant for physical and biological systems in several ways and should be analysed by other long-term proxy data and available model simulations.

Grape harvest dates have been recorded in many European locations for several centuries, and potentially contain important information about past climate. In this study, we systematically analyse the relationship of grape harvest dates recorded in the Burgundy region (France) with different climate data sets in order to understand the connection between climatic conditions and the time of harvest. The results point to a primary dependence of the grape harvest on the temperature from April to August. The strength of this connection depends on the winter to summer temperature relationship and increases over the last 100 years. The grape harvest date is also related to the winter temperature. This connection is non-stationary on interannual, but stable on decadal-to-multidecadal time scales. Therefore, the grape harvest date can be used for independent reconstructions of local April-to-August temperature on interannual time scales as well as remote winter temperature on decadal-to-multidecadal time scales