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Abstract:

Land-cover change (LCC) is an important driver of climate change through carbon emissions (biochemical effects), but also through changes in the surface energy balance (biophysical effects). Quantifying magnitude and sign of surface temperature responses to biophysical effects is still challenging and under debate. We develop a new semi-empirical model based on a linearized surface energy balance for biophysical and an empirical model for the biochemical responses to LCC. Neglecting indirect effects, we find average global direct biophysical and biochemical warmings in response to a stylized deforestation scenario (1.22 K and 0.50 K) and historical LCC (0.42 K and 0.15 K), whereas an afforestation experiment leads to cooling (−1.95 K and −0.96 K). Our results underline the non-negligible impact of biophysical effects, especially non-radiative effects, and stress the importance of including these in the assessment of climate change mitigation and adaptation policies

Abstract:

The ‘signal-to-noise paradox’ for seasonal forecasts of the winter NAO is often described as an ‘underconfident’ forecast and measured using the ratio-of-predictable components metric (RPC). However, comparison of RPC with other measures of forecast confidence, such as spread-error ratios, can give conflicting impressions, challenging this informal description. We show, using a linear statistical model, that the ‘paradox’ is equivalent to a situation where the reliability diagram of any percentile forecast has a slope exceeding 1. The relationship with spread-error ratios is shown to be far less direct. We furthermore compute reliability diagrams of winter NAO forecasts using seasonal hindcasts from the European Centre for Medium-range Weather Forecasts and the UK Meteoro logical Office. While these broadly exhibit slopes exceeding 1, there is evidence of asymmetry between upper and lower terciles, indicating a potential violation of linearity/Gaussianity. The limitations and benefits of reliability diagrams as a diagnostic tool are discussed.

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