Climate processes

Abstract:

The need for high‐precision calculations with 64‐bit or 32‐bit floating‐point arithmetic for weather and climate models is questioned. Lower‐precision numbers can accelerate simulations and are increasingly supported by modern computing hardware. This paper investigates the potential of 16‐bit arithmetic when applied within a shallow water model that serves as a medium complexity weather or climate application. There are several 16‐bit number formats that can potentially be used (IEEE half precision, BFloat16, posits, integer, and fixed‐point). It is evident that a simple change to 16‐bit arithmetic will not be possible for complex weather and climate applications as it will degrade model results by intolerable rounding errors that cause a stalling of model dynamics or model instabilities. However, if the posit number format is used as an alternative to the standard floating‐point numbers, the model degradation can be significantly reduced. Furthermore, mitigation methods, such as rescaling, reordering, and mixed precision, are available to make model simulations resilient against a precision reduction. If mitigation methods are applied, 16‐bit floating‐point arithmetic can be used successfully within the shallow water model. The results show the potential of 16‐bit formats for at least parts of complex weather and climate models where rounding errors would be entirely masked by initial condition, model, or discretization error.

Abstract:

Previous studies have shown that the Lorentz-Lorenz relationship, or molar refractivity/specific refractivity effective medium approximation, enables a reasonable prediction of the refractive index of amorphous water ice, given the refractive index of crystalline water ice. In the current study, we show that the Bruggeman effective medium approximation provides an even closer match to measurements of the refractive index of several amorphous materials, given the refractive index of their crystalline phase. We show that the Bruggeman effective medium approximation provides a good match to measurements of the refractive index of amorphous ice as well. Thus, assuming that the volume fraction of the scattering centers is a constant for a given amorphous material (with respect to a given range of wavelengths) seems to be a more robust assumption than assuming that the molar mass and molar refractivity or specific refractivity are preserved in going from the crystalline state to the amorphous state of the same material. Our results have implications for astrophysics applications, as well as for the optics of non-crystalline materials in general.

Abstract:

Global mean precipitation is expected to increase with increasing temperatures, a process which is fairly well understood. In contrast, local precipitation changes, which are key for society and ecosystems, demonstrate a large spread in predictions by climate models, can be of both signs and have much larger magnitude than the global mean change. Previously, two top-down approaches to constrain precipitation changes were proposed, using either the atmospheric water or energy budget. Here, using an ensemble of 27 climate models, we study the relative importance of these two budgetary constraints and present analysis of the spatial scales at which they hold. We show that specific geographical locations are more constrained by either one of the budgets and that the combination of water and energy budgets provides a significantly stronger constraint on the spatial scale of precipitation changes under anthropogenic climate change (on average about 3000 km, above which changes in precipitation approach the global mean change). These results could also provide an objective way to define the scale of ‘regional’ climate change.