Extreme Months: Multidimensional Studies in the Carpathian Basin

In addition to the one-dimensional mathematical statistical methods used to study the climate and its possible variations, the study of several elements together is also worthwhile. Here, a combined analysis of precipitation and temperature time series was performed using the norm method based on the probability distribution of the elements. This means, schematically speaking, that each component was transformed into a standard normal distribution so that no element was dominant. The transformed components were sorted into a vector, the inverse of the correlation matrix was determined and the resulting norm was calculated. Where this norm was at the maximum, the extreme vector, in this case the extreme month, was found. In this paper, we presented the results obtained from a joint analysis of the monthly precipitation and temperature time series for the whole territory of Hungary over the period 1871–2020. To do this, multidimensional statistical tests that allowed the detection of climate change were defined. In the present analysis, we restricted ourselves to two-dimensional analyses. The results showed that none of the tests could detect two-dimensional climate change on a spatial average for the months of January, April, July and December, while all the statistical tests used indicated a clear change in the months of March and August. As for the other months, one or two, but not necessarily all tests, showed climate change in two dimensions