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Indices of oscillatory behavior are conveniently obtained by projecting the fields in question into a phase space of a few (mostly just two) dimensions; empirical orthogonal functions (EOFs) or other, more dynamical, modes are typically used for the projection. If sufficiently coherent and in quadrature, the projected variables simply describe a rotating vector in the phase space, which then serves as the basis for predictions. Using the boreal summer intraseasonal oscillation (BSISO) as a test case, an alternative procedure is introduced: it augments the original fields with their Hilbert transform (HT) to form a complex series and projects it onto its (single) dominant EOF. The real and imaginary parts of the corresponding complex pattern and index are compared with those of the original (real) EOF. The new index explains slightly less variance of the physical fields than the original, but it is much more coherent, partly from its use of future information by the HT. Because the latter is in the way of real-time monitoring, the index can only be used in cases with predicted physical fields, for which it promises to be superior. By developing a causal approximation of the HT, a real-time variant of the index is obtained whose coherency is comparable to the noncausal version, but with smaller explained variance of the physical fields. In test cases the new index compares well to other indices of BSISO. The potential for using both indices as an alternative is discussed.
A digital filter is introduced which treats the problem of predictability versus time averaging in a continuous, seamless manner. This seamless filter (SF) is characterized by a unique smoothing rule that determines the strength of smoothing in dependence on lead time. The rule needs to be specified beforehand, either by expert knowledge or by user demand. As a result, skill curves are obtained that allow a predictability assessment across a whole range of time-scales, from daily to seasonal, in a uniform manner. The SF is applied to downscaled SEAS5 ensemble forecasts for two focus regions in or near the tropical belt, the river basins of the Karun in Iran and the Sao Francisco in Brazil. Both are characterized by strong seasonality and semi-aridity, so that predictability across various time-scales is in high demand. Among other things, it is found that from the start of the water year (autumn), areal precipitation is predictable with good skill for the Karun basin two and a half months ahead; for the Sao Francisco it is only one month, longer-term prediction skill is just above the critical level.
The literature contains a sizable number of publications where weather types are used to decompose climate shifts or trends into contributions of frequency and mean of those types. They are all based on the product rule, that is, a transformation of a product of sums into a sum of products, the latter providing the decomposition. While there is nothing to argue about the transformation itself, its interpretation as a climate shift or trend decomposition is bound to fail. While the case of a climate shift may be viewed as an incomplete description of a more complex behaviour, trend decomposition indeed produces bogus trends, as demonstrated by a synthetic counterexample with well-defined trends in type frequency and mean. Consequently, decompositions based on that transformation, be it for climate shifts or trends, must not be used.
High precipitation quantiles tend to rise with temperature, following the so-called Clausius-Clapeyron (CC) scaling. It is often reported that the CC-scaling relation breaks down and even reverts for very high temperatures. In our study, we investigate this reversal using observational climate data from 142 stations across Germany. One of the suggested meteorological explanations for the breakdown is limited moisture supply. Here we argue that, instead, it could simply originate from undersampling. As rainfall frequency generally decreases with higher temperatures, rainfall intensities as dictated by CC scaling are less likely to be recorded than for moderate temperatures. Empirical quantiles are conventionally estimated from order statistics via various forms of plotting position formulas. They have in common that their largest representable return period is given by the sample size. In small samples, high quantiles are underestimated accordingly. The small-sample effect is weaker, or disappears completely, when using parametric quantile estimates from a generalized Pareto distribution (GPD) fitted with L moments. For those, we obtain quantiles of rainfall intensities that continue to rise with temperature.