GPS permanent stations KRAW, KATO and ZYWI are part of so called Active Geodetic Network which covers entire area of Upper Silesian Coal Basin (USCB) in Poland and forms precise reference frame for geodetic and geodynamic applications. Moreover the above mentioned stations belong to EUREF Permanent Network. The stations, as datum points, play important role in precise positioning and geoid determination in area of USCB. The study of the stability of these points is one of the main components in precise monitoring of ground deformation in mining areas. The analysis of stability of permanent GPS stations KRAW, KATO and ZYWI are based on the coordinate time series obtained from the EUREF weekly solutions. The relative coordinate time series of weekly solutions for the vectors KRAW - KATO, KRAW - ZYWI , KATO - ZYWI are presented. The consistency, linearity, seasonal variations and jumps in the relative coordinate time series are discussed., Władysław Góral and Jacek Kudrys., and Obsahuje bibliografii
For over 25 years, the International GNSS Service (IGS) has been processing observational data from the Global Navigation Satellite Systems (GNSSs). Hence, long time series of station coordinates are available, however, they are burdened with discontinuities, station velocity changes, and gross errors. Discontinuities and periodic variations are caused by equipment changes at stations, earthquakes, geophysical processes, data problems, as well as local environmental changes. As a result, many approaches have been identified that identify and remove discontinuities in the GNSS coordinate time series. One of them is the program Finding Outliers and Discontinuities In Time Series (FODITS) implemented in the Bernese GNSS Software environment (Dach et al., 2015), developed by the Astronomical Institute, University of Bern. The program is designed for the automatic analysis of time series, in which the functional model is adapted to the time series of coordinates depending on the adopted parameters. This study presents the analysis of long-term GNSS coordinate time series reprocessed in the framework of the realization of the International Terrestrial Reference Frame 2014 (ITRF2014) using the FODITS program. The results show that the optimum confidence level for the autonomous detection of station discontinuities in FODITS is 99% and 98%, for 7-day and 3-day GNSS solutions, respectively, when compared to the manual discontinuity detection from ITRF2014. However, the manual analysis unsupported by statistical tests as conducted in ITRF2014 may contain errors over which further elaboration is indispensable. On the other hand, routine interpretation of GNSS coordinate time series in a fully autonomous manner, although much faster, is not free from drawbacks, in particular in detecting appropriate epochs of discontinuities and changes in station velocities.
In recent years the issue of the natural hydrological and meteorological time series fluctuation has been discussed more and more intensively. As the series of measured hydrological and climatological data become longer and easier worldwide accessible it is possible to deal with a large amount of historical data in their complexity. Handling these data we cannot go without new methods of mathematical statistics and mathematical analysis. In the study some methods of the long-term trends identification in the hydrological time series are presented. Apart from the classical methods, like that of moving averages, the paper focuses in detail on the Hodrick-Prescott (HP) filter. The HP filter is applicable to the trend analysis of the long-term hydrological time series. Next, a new method of the period length identification, the combined periodogramm method, is theoretically developed. Using this method the long cycles length identification becomes more precise. Here, the cycle is considered to be long when it takes the length of about 1/6 to 1/3 of the measured time series. Identification of such long cycles is important with respect to the future hydrospherical processes forecast. Results of application of these methods to the Slovak hydrological time series are presented in the second part of the study. and V posledných rokoch sa začína čoraz viac diskutovať na tému prirodzených fluktuácií hydrologických a meteorologických radov. So stále sa predlžujúcimi radmi meraných hydrologických a klimatických údajov a zlepšujúcim sa prístupom k meraným údajom na celom svete možno komplexnejšie spracovať veľký počet historicky nameraných časových radov. Pri spracovávaní týchto údajov sa nezaobídeme bez rozvoja nových metód štatistiky a matematickej analýzy. V predloženej štúdii boli opísané metódy identifikácie dlhodobého trendu hydrologických radov. Popri už klasických metódach (metóde kĺzavých priemerov) bol v tejto práci rozpracovaný Hodrickov-Prescottov (HP) filter. HP filter možno aplikovať na analýzu trendu dlhodobých ročných hydrologických časových radov. Ďalej bola v štúdii teoreticky rozpracovaná nová metóda identifikácie dĺžky periód časových radov - metóda kombinovaného periodogramu. Uvedená metóda spresňuje identifikáciu dĺžky dlhých cyklov, teda cyklov s dĺžkou okolo 1/6 až 1/3 meraného časového radu. Práve identifikácia týchto dlhých cyklov je veľmi dôležitá pri odhade budúceho vývoja hydrosféry. Praktické použitie uvedených metód na slovenských hydrologických radoch je prezentované v druhej časti štúdie.
In the second part of the paper long-term trends and cyclicity in hydrological time series are identified using both the Hodrick-Presoctt (HP) filter and the combined periodogram. The HP filter seems to be a good tool for analyzing annual time series. It clearly identifies the decrease in the Slovak rainfall time series 1900-1990 and the increase in those of 1990-2000. Using the combined periodogram method oscillation cycles in the discharge time series of main Slovak rivers were identified. These cycles are likely to be characteristic for all Slovak rivers in general. This means the discharge time series are not stationary, they involve a cyclical component. To calculate hydrological characteristics it is necessary to have such a sufficiently long time series that involves both complete wet and dry periods. Because of existence of an about 29 year cycle, a period consisting of 30 years is very suitable. From the long-term point of view, both Danube and Morava Rivers possess steady trends while in the Bodrog and Vah rivers a decrease in discharge occurred during the XX Century. This decrease was mainly due to lower annual rainfalls in Slovakia. When determine long-term discharges, an oscillation of wet and dry periods should be taken into account. The trends should be determined for closed cycles, i.e., either from minimum to minimum or from maximum to maximum. From the long-term trends analysis it follows that the linear trend is not adequate to extrapolate the hydrological time series to the future. and V druhej časti štúdie je identifikovaný dlhodobý trend a cyklickosť slovenských hydrologických časových radov použitím Hodrickovho-Prescottovho (HP) filtra a metódou kombinovaného periodogramu. HP filter sa ukázal byť dobrým nástrojom na analýzu časových radov ročných údajov. Zreteľne identifikuje pokles zrážkových úhrnov na územie SR v období 1900-1990 a nárast úhrnov v rokoch 1990-2000. Metódou kombinovaného periodogramu boli identifikované cykly kolísania prietokových radov najvýznamnejších slovenských tokov. Je pravdepodobné, že tieto cykly sú charakteristické pre všetky slovenské toky. Prietokové rady zahŕňajú v sebe cyklickú zložku. Pri výpočtoch hydrologických charakteristík je potrebné hydrologické charakteristiky počítať z dostatočne dlhých radov zachytávajúcich celý cyklus - mokré i suché obdobie. Tridsaťročné obdobie na výpočet hydrologických charakteristík tokov je vzhľadom na existenciu ca 29-ročného cyklu veľmi vhodné. Z dlhodobého hľadiska Dunaj a Morava majú vyrovnaný trend vodnosti, v Bodrogu a vo Váhu došlo v 20. storočí k poklesu odtoku. Na tomto poklese majú najväčší podiel nižšie ročné zrážkové úhrny na územie SR. Pri určovaní dlhodobých trendov prietokov je potrebné brať do úvahy cykly striedania sa suchých a mokrých období. Vývojové trendy je potrebné určovať za obdobia uzavretých cyklov - od minima po minimum, alebo od maxima po maximum. Z analýzy dlhodobých trendov vyplýva, že použitie lineárneho trendu nie je vhodné na extrapoláciu hydrologických radov do budúcnosti.
In this paper, concepts and techniques of the system theory are used
to obtain state-space (Markovian) models of dynamic economic processes instead of the usual VARMA models. In this respect, the concept of stata is reviewed as are Hankel norm approximations and balanced realizations for stochastic models. We clarify some aspects of the balancing method for state space modelling of the observed time series. This method may fail to satisfy the so-called positive real condition for stochastic processes. We use a statě variance factorization algorithm, which does not require us to solve the algebraic Riccati equation. We relate the Aoki-Havenner method to the Arun-Kung method.
The permanent GPS stations are particulary important for studying various phenomena because they provide uninterrupted measurements allowing to form the time series of station coordinates. Analysis of GPS solutions time series (GPSSTS) for short meridian baselines were explored in the paper (Kryński and Zanimonskiy, 2000). In our article we intend to extend the analysis of the GPSSTS for baselines of different lengths and azimuths. GPS observation data from the ASG-PL network have been used in the research. The GPSSTS in time and frequecy domain have been analyzed. The spectrums of the GPSSTS with the using coherence function were compared. Moreover, a practical approach to correct any unmodeled effects in GPS baseline solutions that cannot be computed using classical GPS adjustment was presented., Władysław Góral and Daniel Jasiurkowski., and Obsahuje bibliografii
Since the formal errors of many geodetic time series are also available, this paper proposes a new singular spectrum analysis (SSA) approach with stabilizing weights (SSAW) by taking the formal errors into account, where the weight of time series data is constructed based on the ratio of formal error to signal power spectrum. The formulae of the proposed SSAW are derived in detail and then used to process the real Global Mean Sea Level (GMSL) time series compared to the traditional SSA. When the first 10 principal components are used to fit the GMSL time series, the fitting errors of the SSAW and traditional SSA are 4.80 mm and 5.14 mm, with the reduction of 6.61 %. According to the 500 simulations based on the reconstructed signals and formal errors of GMSL time series, the mean root mean squared errors and mean absolute errors of reconstructed signals using the SSAW relative to traditional SSA are reduced from 2.18 mm to 1.66 mm and 1.67 mm to 1.34 mm, respectively. Therefore, if the formal errors of a noisy time series given, the proposed SSAW approach is suggested to analyze this time series.