Joint examination of climate time series based on a statistical definition of multidimensional extreme

The joint examination of the climate time series may be efficient methodology for the characterization of extreme weather and climate events. In general, the main difficulties are connected with the different probability distribution of the variables and the handling of the stochastic connection between them. The first problem can be solved by the standardization procedures, i.e., to transform the variables into standard normal ones. For example, there are the Standardized Precipitation Index (SPI) series for the precipitation sums assuming gamma distribution, or the standardization of temperature series assuming normal distribution. In case of more variables, the problem of stochastic connection can be solved on the basis of the vector norm of the transformed variables defined by their covariance matrix. We will present the developed mathematical methodology and some examples for its meteorological applications

Többdimenziós éghajlati idősorok extrémumainak vizsgálata

Az éghajlatváltozás tanulmányozásához elengedhetetlen a szélsőségek vizsgálata. A szélsőségek vizsgálata történhet egyrészt úgy, hogy az extrém éghajlati események idősorát vizsgáljuk, másrészt úgy, hogy az éghajlati idősorok extrémumait vizsgáljuk. Ez utóbbi esetben, ha egyetlen elemet vizsgálunk, a szélsőség az adott idősor maximuma vagy minimuma. Jelen tanulmányban az éghajlati idősorok szélsőértékeit határozzuk meg úgy, hogy több meteorológiai elemet együttesen vizsgálunk és így határozzuk meg az extrémumokat. Rögtön felmerül a kérdés, hogy többdimenziós idősornál van-e értelme szélsőértékről beszélni, és ha igen, milyen módon határozható meg. Ehhez kapcsolódóan bemutatjuk az ún. norma módszert, definiáljuk a vektorváltozó extrémumát, és példákon keresztül mutatjuk be a módszer alkalmazását csapadék- és hőmérséklet-idősorok együttes vizsgálatával. Tanulmányunkhoz a magyarországi napi átlaghőmérsékleti és csapadék idősorokat használtuk fel az 1901‒2019 időszakra. Az alábbiakban bemutatjuk az együttes vizsgálat során kapott legfontosabb eredményeket, és összevetjük az egydimenziós esetben kapott szélsőségekkel. Amennyiben ezzel a módszerrel visszakapjuk az eredeti egydimenziós idősorok szélsőségeit, úgy az éghajlat-változás vizsgálatához nem ad többletet a bemutatni kívánt módszer. Elöljáróban összegezhetjük, hogy elemzéseink azt jelzik, hogy vannak olyan évek, amelyek csak a csapadék vagy csak az átlaghőmérséklet szempontjából nem számítanak extrémnek, de együtt vizsgálva a két elemet mégis kimondhatjuk, hogy szélsőséges évek voltak. Ezek alapján tehát a többdimenziós éghajlati idősorok extrémumainak vizsgálata kiegészíti, és ezáltal hatékonyabbá teszi az éghajlatváltozás vizsgálatát ahhoz képest, mintha csak az egydimenziós idősorokat vizsgálnánk

Creation of a representative climatological database for Hungary from 1870 to 2020

Climate studies, particularly those that are related to climate change, require long, high-quality controlled data sets, which are representative both spatially and temporally. Changing the conditions of measurements, for example relocating the station, or changing the frequency and timing of measurements, or changing the instruments used can cause breaks in the time series. To avoid these problems, data errors and inhomogeneities are eliminated and the data gaps are filled by using the MASH (Multiple Analysis of Series for Homogenization, Szentimrey, 1999, 2008) homogenization procedure. The Hungarian meteorological observation network was upgraded significantly in the last decades. Homogenization of the data series raises the question of how to homogenize long and short data series together within the same process. It is possible to solve this with the MASH method due it has solid mathematical foundations, which make it suitable for such purposes. The solution includes the synchronization of the common parts’ inhomogeneities within three (or more) different MASH processing of the three (or more) datasets with different lengths depending on the time periods and elements. After the homogenization process, the station data series were interpolated to a 0.1 degree regular grid covering the whole area of Hungary. The MISH (Meteorological Interpolation based on Surface Homogenized Data Basis; Szentimrey and Bihari, 2007) program system was used for this purpose. The MISH procedure was developed specifically for the interpolation of various meteorological elements. In the case of mean temperature, we also renewed the MISH modeling, as compared to previous years, the number of homogenized stations doubled due to the new work, so it was expedient to model the climate statistical parameters with this extended station system. Time series of daily mean temperature and precipitation sum for the period 1870–2020 for Hungary were used in this study. As a result, the longest ever homogenized, gridded daily data sets became available for Hungary. The method described here can also be applied to produce representative datasets for other meteorological elements

Development of new version MASHv4.01 for homogenization of standard deviation

The earlier versions of our method MASH (Multiple Analysis of Series for Homogenization; Szentimrey) were developed for homogenization of the daily and monthly data series in the mean, i.e., the first order moment. The software MASH was developed as an interactive automatic, artificial intelligence (AI) system that simulates the human intelligence and mimics the human analysis on the basis of advanced mathematics. This year we finished the new version MASHv4.01 that is able to homogenize also the standard deviation, i.e., the second order moment. The problem of standard deviation is related to the monthly and daily data series homogenization

Statistical modeling of the present climate by the interpolation method MISH – theoretical considerations

Our method MISH (Meteorological Interpolation based on Surface Homogenized Data Basis; Szentimrey and Bihari) was developed for spatial interpolation of meteorological elements. According to mathematical theorems, the optimal interpolation parameters are known functions of certain climate statistical parameters, which fact means we could interpolate optimally if we knew the climate. Furthermore, the data assimilation methods also need to know the climate if Bayesian estimation theory is to be correctly applied. Therefore, we have developed the MISH system also to model the climate statistical parameters, i.e. present climate, by using long data series. It is a nonsense that we try to model the future climate but we do not know the present climate

Republic of Macedonia -25

Abstract The MISH (Meteorological Key words: SPI, interpolation, MISH, gridding The MISH method The MISH (Meteorological Interpolation based on Surface Homogenized Data Basis) method for the spatial interpolation of surface meteorological elements was developed at the Hungarian Meteorological Service . This is a meteorological system not only in respect of the aim but in respect of the tools as well. It means that using all the valuable meteorological information -climate and supplementary model or background information -is intended. For that purpose developing an adequate mathematical background was also necessary of course. In the practice many kinds of interpolation methods exist therefore the question is the difference between them. According to the interpolation problem the unknown predictand value is estimated by using the known predictor values. The type of the adequate interpolation formula depends on the probability distribution of the meteorological elements! Additive formula is appropriate for normal distribution (e.g. temperature) while some multiplicative formula can be applied for quasi lognormal distribution (e.g. precipitation). The expected interpolation error depends on certain interpolation parameters as for example the weighting factors. The optimum interpolation parameters minimize the expected interpolation error and these parameters are certain known functions of different climate statistical parameters e.g. expectations, deviations and correlations. Consequently the modelling of the climate statistical parameters is a key issue to the interpolation of meteorological elements. The various geostatistical kriging methods applied in GIS are also based on the above mathematical theory -To model the climate statistical parameters by using long homogenized data series. -To calculate the modeled optimum interpolation parameters which are certain known functions of the modeled climate statistical parameters

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