Predictability of weather and climate

Abstract:

Posit numbers, a recently proposed alternative to floating-point numbers, claim to have smaller arithmetic rounding errors in many applications. By studying weather and climate models of low and medium complexity (the Lorenz system and a shallow water model) we present benefits of posits compared to floats at 16 bit. As a standardised posit processor does not exist yet, we emulate posit arithmetic on a conventional CPU. Using a shallow water model, forecasts based on 16-bit posits with 1 or 2 exponent bits are clearly more accurate than half precision floats. We therefore propose 16 bit with 2 exponent bits as a standard posit format, as its wide dynamic range of 32 orders of magnitude provides a great potential for many weather and climate models. Although the focus is on geophysical fluid simulations, the results are also meaningful and promising for reduced precision posit arithmetic in the wider field of computational fluid dynamics.

Abstract:

The North Atlantic sector has been identified as a region where the 11‐year solar cycle has small but potentially non‐negligible impacts on winter climate, but a debate persists about the robustness of such impacts. This work explores the signatures of the 11‐year solar cycle over the North Atlantic in the ERA5 and 20th Century Reanalysis datasets. The results confirm previous studies with a robust positive boreal winter response in mean‐sea‐level pressure (mslp) in the region of the Azores at lags of three years after solar maximum. The spatial evolution of the response is examined in detail by first decomposing the mslp time series into the dominant modes of North Atlantic winter mslp variability, including the North Atlantic Oscillation (NAO), the East Atlantic (EA) and the Scandinavian patterns, before performing a multilinear regression analysis. We find that the maximum 11‐year solar response in the December–January–February (DJF) average does not project directly onto the NAO. However, when the early/late‐winter responses are examined separately, a statistically significant NAO response is seen in late winter (January–February) at lag 0–1 years and a statistically significant NAO response is also seen at lag +3 years in early winter (November–December). These results are consistent with predicted responses from previously proposed top‐down influences from the stratosphere in late winter followed by the re‐emergence of a signal from underlying sea surface temperatures in early winter. However, the NAO response is not the primary contributor to the total DJF response at lag +3 years. A previously unidentified solar‐cycle response in the EA pattern is found in late winter at lag +3 years with larger amplitude than the NAO response. The evolution of the DJF mslp response over the Azores region can thus be understood as a summation of the NAO and EA patterns at lag +3 years.

Abstract:

Cities worldwide are increasingly facing the challenges of heat stress, a problem expected to worsen with ongoing climate change. The lack of detailed, city-specific data hinders effective response measures and limits the adaptive capacity of urban populations. In this data descriptor, we introduce a comprehensive database providing climate and heat stress information for 142 cities globally, covering the present and extending projections up to 2100 across three distinct climate scenarios, including two overshoot scenarios. This dataset includes 34 heat stress indicators at a spatial resolution of 100 meters, offering a unique database to identify vulnerable areas and deepen the understanding of urban heat risks. The data is presented through an accessible, user-friendly dashboard, enabling policymakers, researchers, and city planners, as well as non-experts, to easily visualise and interpret the findings, supporting more informed decision-making and urban adaptation strategies.

Abstract:

Motivated in part by John Wheeler's assertion that the continuum nature of Hilbert Space conceals the "it-from-bit" information-theoretic character of the quantum wavefunction, a theory of quantum physics (Rational Quantum Mechanics-RaQM) is proposed based on a specific discretization of complex Hilbert Space. The Schrödinger equation is not modified in RaQM, even during measurement. However, the bases in which the quantum state is defined must satisfy certain rational-number constraints. These constraints lead to the notion of finite qubit information capacity [Formula: see text]: For any [Formula: see text] qubit state, there is insufficient information in the [Formula: see text] qubits (linearly growing in [Formula: see text]) to allocate even one bit to each of all [Formula: see text] continuum degrees of freedom (exponentially growing in [Formula: see text]) associated with quantum mechanics/theory (QM, where [Formula: see text]). It is proposed that the discretization of Hilbert Space in RaQM is due to gravity, hence QM is the (singular) continuum limit of RaQM at [Formula: see text]. On this basis, it is estimated that [Formula: see text] lies between about 200 and 400 for current qubit technologies, and will never exceed 1,000. While QM and RaQM are experimentally indistinguishable for small numbers of qubits, RaQM predicts that the exponential advantage of quantum algorithms which, like Shor's, require bases with maximal [Formula: see text]-qubit superposition/entanglement, will have saturated at 1,000 perfect qubits. Hence, insofar as a classical computer will never factor a 2,048-bit RSA integer, RaQM predicts that a quantum computer will not either. This predicted breakdown of QM could be testable in less than 5 y.

Abstract:

Nudging still is a cost-effective data assimilation technique in coupled climate models, but conventional schemes apply fixed spatial strengths and are less effective in representing heterogeneous ocean processes. An adaptive nudging framework based on a spatially varying gain matrix is proposed to dynamically balance model and observational errors. The method not only preserves the merits of the latitude-dependent nudging approach but also provides a more physically consistent determination of the spatial distribution of nudging coefficients. Implemented in the SPEEDY-NEMO coupled model, the framework is systematically evaluated against the traditional latitude-dependent scheme. Results show that the adaptive approach substantially improves subsurface temperature assimilation, particularly in the Niño3.4 region, the tropical Indian Ocean, North Pacific, North Atlantic, and the northeastern Pacific. In the tropics, the improvement is mainly achieved above and within the thermocline (roughly 100--200 m), where strong vertical stratification and sharp gradients make fixed nudging strengths inadequate:the RMSE decreases by 20% and the correlation with observations increases by 30% compared with the traditional latitude-dependent scheme. By dynamically adjusting the assimilation strength, the adaptive scheme better constrains the thermocline variability and surface-subsurface interactions. In mid- to high-latitude regions, the improvement extends to greater depths, consistent with a deeper thermocline, where oceanic processes dominated by the mixed layer dynamics and convection exhibit large regional biases that require spatially adaptive correction. In addition, compared with the latitude-dependent nudging scheme, the adaptive approach achieves simultaneous corrections of both the systematic bias term and the variance term of temperature deviations, thereby enhancing not only the mean state but also the model’s ability to capture variability. Generally, the root-mean-square errors decrease by 20-30% and the correlation with observations increases around 30-50% by the adaptive scheme. Beyond temperature, improvements are also evident in salinity, currents, and sea surface height anomalies, indicating the broader benefits of the adaptive scheme. These results indicate that spatially adaptive nudging provides a more effective and practical alternative to fixed schemes, offering a solid basis for improving ocean state estimation in coupled models.