Predictability of weather and climate

Abstract:

Non-periodic solutions are an essential property of chaotic dynamical systems. Simulations with deterministic finite-precision numbers, however, always yield orbits that are eventually periodic. With 64-bit double-precision floating-point numbers such periodic orbits are typically negligible due to very long periods. The emerging trend to accelerate simulations with low-precision numbers, such as 16-bit half-precision floats, raises questions on the fidelity of such simulations of chaotic systems. Here, we revisit the 1-variable logistic map and the generalised Bernoulli map with various number formats and precisions: floats, posits and logarithmic fixed-point. Simulations are improved with higher precision but stochastic rounding prevents periodic orbits even at low precision. For larger systems the performance gain from low-precision simulations is often reinvested in higher resolution or complexity, increasing the number of variables. In the Lorenz 1996 system, the period lengths of orbits increase exponentially with the number of variables. Moreover, invariant measures are better approximated with an increased number of variables than with increased precision. Extrapolating to large simulations of natural systems, such as million-variable climate models, periodic orbit lengths are far beyond reach of present-day computers. Such orbits are therefore not expected to be problematic compared to high-precision simulations but the deviation of both from the continuum solution remains unclear

Abstract:

Increasing atmospheric moisture content is expected to intensify precipitation extremes under climate warming. However, extreme precipitation sensitivity (EPS) to temperature is complicated by the presence of reduced or hook-shaped scaling, and the underlying physical mechanisms remain unclear. Here, by using atmospheric reanalysis and climate model projections, we propose a physical decomposition of EPS into thermodynamic and dynamic components (i.e., the effects of atmospheric moisture and vertical ascent velocity) at a global scale in both historical and future climates. Unlike previous expectations, we find that thermodynamics do not always contribute to precipitation intensification, with the lapse rate effect and the pressure component partly offsetting positive EPS. Large anomalies in future EPS projections (with lower and upper quartiles of -1.9%/°C and 8.0%/°C) are caused by changes in updraft strength (i.e., the dynamic component), with a contrast of positive anomalies over oceans and negative anomalies over land areas. These findings reveal counteracting effects of atmospheric thermodynamics and dynamics on EPS, and underscore the importance of understanding precipitation extremes by decomposing thermodynamic effects into more detailed terms.