Abstract.We investigated the usability of the method of local linear models (LLM), multilayer perceptron neural network (MLP NN) and radial basis function neural network (RBF NN) for the construction of temporal and spatial transfer functions between different meteorological quantities, and compared the obtained results both mutually and to the results of multiple linear regression (MLR). The tested methods were applied for the short-term prediction of daily mean temperatures and for the downscaling of NCEP/NCAR reanalysis data, using series of daily mean, minimum and maximum temperatures from 25 European stations as predictands. None of the tested nonlinear methods was recognized to be distinctly superior to the others, but all nonlinear techniques proved to be better than linear regression in the majority of the cases. It is also discussed that the most frequently used nonlinear method, the MLP neural network, may not be the best choice for processing the climatic time series -LLM method or RBF NNs can offer a comparable or slightly better performance and they do not suffer from some of the practical disadvantages of MLPs.Aside from comparing the performance of different methods, we paid attention to geographical and seasonal variations of the results. The forecasting results showed that the nonlinear character of relations between climate variables is well apparent over most of Europe, in contrast to rather weak nonlinearity in the Mediterranean and North Africa. No clear large-scale geographical structure of nonlinearity was identified in the case of downscaling. Nonlinearity also seems to be noticeably stronger in winter than in summer in most locations, for both forecasting and downscaling.
ABSTRACT:This article introduces areal analysis of regular changes in 500-hPa temperature fields with pseudo-2D wavelet transform (p2D-WT). p2D-WT is a new technique, a practical approach based on the 1D continuous wavelet transform (CWT), designed to describe frequency characteristics of studied datasets in terms of their evolution in both time and space. The algorithm transforms datasets defined in a grid into a multidimensional object, which is subsequently interpreted by time and frequency slices. In this study, we describe the transformation fundamentals and application of the transform on the 500-hPa temperature field. Two types of reanalysis data are studied: time series from the European Centre for Medium-Range Weather Forecasts (denoted as ERA-40) and datasets from National Centers for Environmental Prediction and National Center for Atmospheric Research (NCEP/NCAR). The analysis of the climatological data shows the presence of various periodicities among which the most distinct are the annual cycle (AC), semi-annual cycle, quasiquadrennial oscillation (QQO) and quasi-decadal oscillation (QDO). The article also provides a comparison of frequency characteristics of the NCEP/NCAR and ERA-40 reanalysis datasets; it shows that the frequency patterns found in the particular reanalysis datasets differ only in limited areas.
Abstract:The growth of small errors in weather prediction is exponential on average. As an error becomes larger, its growth slows down and then stops with the magnitude of the error saturating at about the average distance between two states chosen randomly. This paper studies the error growth in a low-dimensional atmospheric model before, during and after the initial exponential divergence occurs. We test cubic, quartic and logarithmic hypotheses by ensemble prediction method. Furthermore, the quadratic hypothesis suggested by Lorenz in 1969 is compared with the ensemble prediction method. The study shows that a small error growth is best modeled by the quadratic hypothesis. After the error exceeds about a half of the average value of variables, logarithmic approximation becomes superior. It is also shown that the time length of the exponential growth in the model data is a function of the size of small initial error and the largest Lyapunov exponent. We conclude that the size of the error at the least upper bound (supremum) of time length is equal to 1 and it is invariant to these variables. Predictability, as a time interval, where the model error is growing, is for small initial error, the sum of the least upper bound of time interval of exponential growth and predictability for the size of initial error equal to 1.
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