Changes in the Probability of Heavy Precipitation: Important Indicators of Climatic Change

A simple statistical model of daily precipitation based on the gamma distribution is applied to summer (JJA in Northern Hemisphere, DJF in Southern Hemisphere) data from eight countries: Canada, the United States, Mexico, the former Soviet Union, China, Australia, Norway, and Poland. These constitute more than 40% of the global land mass, and more than 80% of the extratropical land area. It is shown that the shape parameter of this distribution remains relatively stable, while the scale parameter is most variable spatially and temporally. This implies that the changes in mean monthly precipitation totals tend to have the most influence on the heavy precipitation rates in these countries. Observations show that in each country under consideration (except China), mean summer precipitation has increased by at least 5% in the past century. In the USA, Norway, and Australia the frequency of summer precipitation events has also increased, but there is little evidence of such increases in any of the countries considered during the past fifty years. A scenario is considered, whereby mean summer precipitation increases by 5% with no change in the number of days with precipitation or the shape parameter. When applied in the statistical model, the probability of daily precipitation exceeding 25.4 mm (1 inch) in northern countries (Canada, Norway, Russia, and Poland) or 50.8 mm (2 inches) in mid-latitude countries (the USA, Mexico, China, and Australia) increases by about 20% (nearly four times the increase in mean). The contribution of heavy rains (above these thresholds) to the total 5% increase of precipitation is disproportionally high (up to 50%), while heavy rain usually constitutes a significantly smaller fraction of the precipitation events and totals in extratropical regions (but up to 40% in the tropics, e.g., in southern Mexico). Scenarios with moderate changes in the number of days with precipitation coupled with changes in the scale parameter were also investigated and found to produce smaller increases in heavy rainfall but still support the above conclusions. These scenarios give changes in heavy rainfall which are comparable to those observed and are consistent with the greenhouse-gas-induced increases in heavy precipitation simulated by some climate models for the next century. In regions with adequate data coverage such as the eastern two-thirds of contiguous United States, Norway, eastern Australia, and the European part of the former USSR, the statistical model helps to explain the disproportionate high changes in heavy precipitation which have been observed.     

Kustaanheimo–Stiefel transformation with an arbitrary defining vector

Kustaanheimo–Stiefel (KS) transformation depends on the choice of some preferred direction in the Cartesian 3D space. This choice, seldom explicitly mentioned, amounts typically to the direction of the first or the third coordinate axis in Celestial Mechanics and atomic physics, respectively. The present work develops a canonical KS transformation with an arbitrary preferred direction, indicated by what we call a defining vector. Using a mix of vector and quaternion algebra, we formulate the transformation in a reference frame independent manner. The link between the oscillator and Keplerian first integrals is given. As an example of the present formulation, the Keplerian motion in a rotating frame is re-investigated.     

Traffic transformer: Capturing the continuity and periodicity of time series for traffic forecasting

Traffic forecasting is a challenging problem due to the complexity of jointly modeling spatio‐temporal dependencies at different scales. Recently, several hybrid deep learning models have been developed to capture such dependencies. These approaches typically utilize convolutional neural networks or graph neural networks (GNNs) to model spatial dependency and leverage recurrent neural networks (RNNs) to learn temporal dependency. However, RNNs are only able to capture sequential information in the time series, while being incapable of modeling their periodicity (e.g., weekly patterns). Moreover, RNNs are difficult to parallelize, making training and prediction less efficient. In this work we propose a novel deep learning architecture called Traffic Transformer to capture the continuity and periodicity of time series and to model spatial dependency. Our work takes inspiration from Google’s Transformer framework for machine translation. We conduct extensive experiments on two real‐world traffic data sets, and the results demonstrate that our model outperforms baseline models by a substantial margin.     

A multiyear analysis of aerosol optical thickness over Europe and Central Poland using NAAPS model simulation

This study contains a comparative analysis of aerosol optical thickness (AOT) between numerical calculations obtained from the Navy Aerosol Analysis and Prediction System (NAAPS) model and direct observations from the AERONET robotic network and the Saharan Aerosol over WArsaw (SAWA) field campaign. AOT was calculated for 500 nm wavelength. The comparison shows underestimation of the total aerosol optical thickness simulated by NAAPS. The correlation coefficients between model and observation oscillates between 0.57 and 0.72. Results of seven-year (1998–2004) NAAPS simulation of aerosol components (sea salt, mineral dust, sulphate, and smoke) show large temporal and spatial variability of the aerosol optical thickness over Europe. The least polluted region is the Iberian Peninsula, while the highest aerosol burdens occurred in Central Europe, mostly due to anthropogenic sulphate particles. Finally, the analysis of mineral dust transport shows frequent episodes of Saharan dust inflow over Central Europe. There are about 20 days a year (4 days in May) when instantaneous AOT associated with mineral dust aerosol increases over 0.1.