István Gábor Hatvani

Classification into homogeneous groups using combined cluster and discriminant analysis

Abstract The classification of observations into groups is a general procedure in modern research. However, when searching for homogeneous groups the difficulty of deciding whether further division of a classification is necessary or not to obtain the desired homogeneous groups arises. The presented method, Combined cluster and discriminant analysis (CCDA), aims to facilitate this decision. CCDA consists of three main steps: (I) a basic grouping procedure; (II) a core cycle where the goodness of preconceived and random classifications is determined; and (III) an evaluation step where a decision has to be made regarding division into sub-groups. These steps of the proposed method were implemented in R in a package, under the name of ccda. To present the applicability of the method, a case study on the water quality samples of Neusiedler See is presented, in which CCDA classified the 33 original sampling locations into 17 homogeneous groups, which could provide a starting point for a later recalibration of the lakes monitoring network.

The Water Framework Directive: Can more information be extracted from groundwater data? A case study of Seewinkel, Burgenland, eastern Austria

Water protection is one of the most important goals in environmental protection. The Clean Water Act in the USA and the Water Framework Directive (WFD) in Europe are the legal frameworks to facilitate the achievement of this goal. The question is raised of whether more information can be extracted from WFD-related groundwater data. To answer it, a methodology has been developed that is easy to use and could be implemented into official practice. A case study is presented in which the groundwater data of a sodic area in Austria (Seewinkel) is assessed. Eighteen parameters in groundwater sampled from 23 wells (1991–2011) were analyzed. With basic statistics, trend-, cluster-, Wilks’ λ and spatial sampling density analysis, local phosphorus and boron phenomena were described, along with the determining role of sulphate, groundwater flow, and the oxygen gradient in the area. As a final step, the spatial sampling density was determined. Regarding the current set of parameters, all the sampling sites are necessary and only in the case of certain parameters (Ca2+, Mg2+, K+, NO3−, pH) could one sampling site be abandoned. The methodology applied brings a new perspective to exploring groundwater data collected according to the requirements of the WFD.ZusammenfassungGewässerschutz ist eines der wichtigsten Ziele im Umweltschutz. Der “Clean Water Act” in den USA und die Wasserrahmenrichtlinie (WRRL) in Europa sind die rechtlichen Rahmenbedingungen, um dieses Ziel zu erreichen. Dabei stellt sich die Frage, ob weitere verbesserte Informationen aus den derzeitigen Grundwasserqualitätsmessungen, die im Rahmen der WRRL erhoben werden, gewonnen werden können. Um diese Frage zu beantworten, wurde eine Methodik entwickelt, die einfach zu bedienen ist und leicht in die offizielle Auswertungspraxis umgesetzt werden könnte. In der vorgestellten Fallstudie wurden die Daten eines Grundwasserkörpers in Österreich (Seewinkel) mit der entwickelten Methode ausgewertet. Dazu wurden achtzehn Parameter aus 23 Grundwassergütemessstellen für die Jahre 1991–2011 analysiert. Dazu wurden grundlegende statistische Methoden wie Trend -, Cluster -, Wilks’ λ Analyse und die Auswertung der räumlichen Verteilung der Messdichte verwendet. Unter Berücksichtigung mit der bestimmenden Rolle von Sulfat, der Grundwasserfließrichtung und -zeit und dem Sauerstoffgradienten im Untersuchungsgebiet Seewinkel konnten lokale Phosphor und Bor Phänomene beschrieben werden. Im letzten Schritt wurde die räumliche Verteilung der Messdichte bestimmt. Die Datenanalysen zeigten, dass alle, bis auf eine Ausnahme, vorhandenen Messstellen und deren Parameter (Ca2+, Mg2+, K+, NO3−, pH-Wert) für Auswertungen verwendet werden konnten. Die angewandte Methodik bringt bei der Analyse der erhobenen Grundwasserqualitätsdaten, welche nach den Anforderungen der WRRL erhoben werden, eine neue Perspektive.RésuméLa protection de l’eau est l’un des objectifs les plus importants de la protection environnementale. Le Clean Water Act aux Etats Unis et la Directive-Cadre sur l’Eau (DCE) en Europe sont les cadres légaux pour favoriser l’atteinte de cet objectif. La question est posée de savoir si l’on peut tirer d’avantages d’informations des données sur l’eau souterraine relatives à la DCE. Pour répondre à celle-ci, on a développé une méthodologie simple, pouvant être mise en pratique de façon officielle. Le cas présenté considère les données sur l’eau souterraine d’un district sodique d’Autriche (Seewinkel). Dix huit paramètres de l’eau de 23 puits échantillonnés (1991–2011) ont été analysés. Avec les paramètres statistiques de base, tendance, classes, paramètre λ de Wilks et analyse de la densité spatiale d’échantillonnage, les phénomènes locaux liés au phosphore et au bore ont été décrits, ainsi que le rôle déterminant du sulfate, le flux d’écoulement souterrain et le gradient de l’oxygène dans la zone. En phase finale, la densité d’échantillonnage spatial a été déterminée. Etant donné le jeu de paramètres considérés, tous les sites échantillonnés sont nécessaires, les sites où certains paramètres (Ca2+, Mg2+, K+, NO3−, pH) ne pouvaient être mesurés étant abandonnés. La méthodologie appliquée ouvre une nouvelle perspective dans l’exploitation des données sur l’eau souterraine prélevées selon les dispositions de la Directive-Cadre sur l’Eau.ResumenLa protección del agua es uno de los objetivos más importantes en la protección ambiental. La Ley de Aguas Limpias en EEUU y la Directiva Marco del Agua (WFD) en Europa son los marcos legales para facilitar el logro de este objetivo. La cuestión se plantea si se puede extraer mayor información de los datos de agua subterránea relacionados con WDF. Para responder se desarrolla una una metodología que es fácil de usar y podría ser implementada dentro de la práctica oficial. Se presenta un caso de estudio en el cual se evaluaron los datos de agua subterránea de un área sódica en Austria (Seewinkel). Se analizaron dieciocho parámetros en el agua subterránea muestreada de 23 pozos (1991–2011). Con estadísticas básicas, tendencias, clusters, Wilks’ λ y análisis de densidad espacial de muestreo se describieron los fenómenos locales de fósforo y de boro fueron descriptos, conjuntamente con el rol determinante del sulfato, del flujo de agua subterránea, y del gradiente de oxígeno en el área. Como una etapa final, se determinó la densidad de muestreo espacial. En relación con el conjunto actual de parámetros, todos los sitios de muestreos son necesarios y solamente en el caso de ciertos parámetros (Ca2+, Mg2+, K+, NO3−, pH) podría un sitio de muestreo ser abandonado. La metodología aplicada otorga una nueva perspectiva para explorar los datos de agua subterránea recolectados de acuerdo a los requerimientos de la WFD.الملخصحماية المياه هي واحدة من اهم الاهداف في الحماية البيئية. قانون المياه النظيفة في الولايات المتحدة الامريكية والاطار التوجيهي للمياه(WFD) في اوروبا هما من الاطر القانونية لتسهيل تحقيق هذا الهدف . اثيرت مسألة ما اذا كان مزيد من المعلومات يمكن استخصلاصها من الاطار التوجيهي للمياه (WFD) – المتعلقة ببيانات المياه الجوفية. للاجابة على ذلك ، تم تطوير منهجية سهلة الاستخدام ويمكن تنفيذها في الممارسة الرسمية . قدمت دراسة الحالة التي يتم فيها تقييم بيانات المياه الجوفية من منطقة سوديك في النمسا .(Seewinkel) حللت ثمانية عشر معيارا في المياه الجوفية قد تم اخذ عيناتها من ٢٣ بئرا (١٩٩١-٢٠١١).مع احصائية بسيطة، الاتجاه ،الكتلة ، ويلكس λ ومكانية تحليل كثافة اخذ العينات . ظاهرة الفوسفور والبورون المحلية قد وصفت جنبا الى جنب مع دور تحديد الكبريتات ، تدفق المياه الجوفية، والتدرج الاوكسجين في المنطقة . كخطوة نهائية ، تم تحديد كثافة اخذ العينات المكانية . وفيما يتعلق المجموعة الحالية من المعاير ، جميع مواقع اخذ العينات ضرورية و فقط في حالة معايير معينة (Ca2+, Mg2+, K+, NO3-, pH) يمكن ان يتم التخلي عن موقع واحد.المنهجية المطبقة يجلب منظورا جديدا لاستكشاف بيانات المياه الجوفية التي تم جمعها وفق لمتطلبات الاطار التوجيهي للمياه (WFD) .摘要水保护是环境保护中最重要的目标之一。美国的清洁水法及欧洲水框架指令是促进完成这个目标的法律体系。是否能从水框架指令有关的地下水数据中提取更多信息的问题被提了出来。为回答这个问题,开发了便于使用、能够正式实施的方法。展示了一个研究实例,在这个实例中,评价了奥地利(Seewinkel)含钠区的地下水数据。分析了23口井(1991–2011年)中地下水样品的十八个参数。描述了基本统计数字以及趋势的、簇群的Wilks’ λ、空间采样密度分析、局部磷和硼现象,并确定了该区的硫酸盐的作用、地下水流和氧梯度。作为最后一步,确定了空间采样密度。关于目前参数(Ca2+, Mg2+, K+, NO3−, pH)的设置,所有的采样地点都很必要,只有在某些参数情况下,一个采样点可以放弃。所应用的方法给探索按照水框架指令要求收集到的地下水数据带来了新的前景。SamenvattingWater bescherming is een van de belangrijkste doelen in bescherming van het milieu. De Clean Water Act in de Verenigde Staten en de Water Framework Directive in Europa zijn de wettelijke kaders waarin deze doelen worden bereikt. De vraag is opgekomen of meer informatie verkregen kan worden van WFD gerelateerde grondwater data. Om deze vraag te beantwoorden is een methode ontwikkeld die makkelijk te gebruiken is en geimplementeerd kan worden door officiele instanties. Een case study wordt gepresenteerd waarin grondwater data van een alkali regio in Oostenrijk (Seewinkel) wordt beoordeeld. Achttien parameters in grondwater bemonsterd in 23 verschillende peilbuizen (1991–2011) zijn geanalyseerd. Met behulp van basis statistiek, trend-, cluster-, Wilks’ λ en ruimtelijke bemonster dichtheid analyses, werden lokale fosfor en boor fenomenen beschreven, net als de bepalende rol van sulfaat, grondwater stroming, en de zuurstof gradient in het onderzoeksgebied. Als laatste stap werd de ruimtelijke bemonster dichtheid bepaald. Met betrekking tot de huidige set aan parameters, waren alle bemonsteringsplekken noodzakelijk. Slechts bij sommige parameters (Ca2+, Mg2+, K+, NO3-, pH) kon één bemonsteringsplek worden opgegeven. De gebruikte methodologie geeft een nieuw perspectief aan het onderzoeken van grondwater data die verzameld zijn volgens de eisen van de WFD. KivonatA felszíni és felszín alatti vizeink jó állapotban való megőrzése a környezetvédelem egyik legfontosabb célja. Az Amerikai Egyesült Államokban a “Clean Water Act”, Európában pedig a Víz Keretirányelv biztosítja a jogi keretet ezen célok eléréséhez. Felmerül azonban a kérdés, hogy hordoznak-e számottevő többletinformációt a felszín alatti víz monitoring adatok a Víz Keretirányelv által előírt vizsgálatok eredményein túl. A kérdés megválaszolására egy olyan módszertant dolgoztunk ki, amely könnyen alkalmazható a környezetvédelmi hivatali gyakorlatban is. Esettanulmányként, egy ausztriai szikes terület (Seewinkel) 23 felszín alatti víz monitoring kútjának 18 paraméterének idősorait dolgoztuk fel az 1991–2011-es időintervallum vonatkozásában alap- és Wilks’ λ statisztikák, valamint trend-, klaszter-, és variogram analízis felhasználásával. Az eredmények alapján a terület bizonyos részein lokális foszfor, bór és szulfát anomália, illetve az egész területre vonatkozó oxigén gradiens figyelhető meg. Végezetül meghatároztuk a szükséges térbeli mintavételezési gyakoriságot. Az összes mért paramétert figyelembe véve minden mintavételi pontra szükség van a területen, csak néhány paraméter vonatkozásában (Ca2+, Mg2+, K+, NO3−, pH) lehetne egy mintavételi pontot megszüntetni. Az alkalmazott módszertan egy újszerű megk

Analysis of Water Quality Data for Scientists

The most often used models are deterministic, although they are prepared from one sampling event. It must be stated that the statistics and model results obtained from this sampling event can significantly change if the sampling is to be reproduced because their results are probability variables (Kovacs & Szekely, 2006). In the case of deterministic models this problem is solved by means of sensitivity analyses, thus the uncertainty in the applied model remains. This may be the reason why the following can be found in the international literature regarding this question: “The future is stochastic modeling” (Kovacs & Szanyi, 2005; Wilkinson, 2006).

Spatial Optimization of Monitoring Networkson the Examples of a River, a Lake-Wetland System and a Sub-Surface Water System

Monitoring systems in general have to meet numerous requirements, the most important of which are representativeness and cost efficiency. The aim of the study, therefore, was to present the spatial optimization of the monitoring networks of a river (the Danube), a wetland-lake system (Kis-Balaton & Lake Balaton), and a sub-surface water system in the watershed of Lake Neusiedl/Fertő over a period of approximately two decades using a novel method, Combined cluster and discriminant analysis (CCDA). In the case of the river the results show that the monitoring network yields redundant information on certain sections, so that of 12 sampling sites 3 can be discarded. It was not, however, enough to consider just the tributaries when it comes to optimization. In the case of the wetland (Kis-Balaton) one pair of sampling sites out of 12, while in the case of Lake Balaton 5 out of 10 can be abandoned. For the sub-surface water system, however, all the 50 sites contained exclusive information; hence, all of these were shown to be necessary. In addition, neighboring sampling sites were compared pairwise using CCDA and the corresponding results were visualized in diagrams or so called “difference maps” indicating the location of the biggest differences. This approach also indicates the researcher where to place new sampling sites should the possibility arise. The discussed methodology proved to be highly useful in the optimization of the monitoring networks of the presented water systems.

Detecting breakpoints in artificially modified- and real-life time series using three state-of-the-art methods

Abstract Time series often contain breakpoints of different origin, i.e. breakpoints, caused by (i) shifts in trend, (ii) other changes in trend and/or, (iii) changes in variance. In the present study, artificially generated time series with white and red noise structures are analyzed using three recently developed breakpoint detection methods. The time series are modified so that the exact “locations” of the artificial breakpoints are prescribed, making it possible to evaluate the methods exactly. Hence, the study provides a deeper insight into the behaviour of the three different breakpoint detection methods. Utilizing this experience can help solving breakpoint detection problems in real-life data sets, as is demonstrated with two examples taken from the fields of paleoclimate research and petrology.

A Special Issue: Geomathematics in practice: Case studies from earth- and environmental sciences – Proceedings of the Croatian-Hungarian Geomathematical Congress, Hungary 2015

Abstract The present paper aims to introduce the current problems of geomathematics along with giving on overview on the papers published in the special issue covering the Croatian-Hungarian Geomathematical Congress of 2015 in Hungary.

Geostatistical screening of flood events in the groundwater levels of the diverted inner delta of the Danube River: implications for river bed clogging

Abstract The efficient operation of shallow groundwater (SGW) monitoring networks is crucial to water supply, in-land water protection, agriculture and nature conservation. In the present study, the spatial representativity of such a monitoring network in an area that has been thoroughly impacted by anthropogenic activity (river diversion/damming) is assessed, namely the Szigetköz adjacent to the River Danube. The main aims were to assess the spatial representativity of the SGW monitoring network in different discharge scenarios, and investigate the directional characteristics of this representativity, i.e. establish whether geostatistical anisotropy is present, and investigate how this changes with flooding. After the subtraction of a spatial trend from the time series of 85 shallow groundwater monitoring wells tracking flood events from 2006, 2009 and 2013, variography was conducted on the residuals, and the degree of anisotropy was assessed to explore the spatial autocorrelation structure of the network. Since the raw data proved to be insufficient, an interpolated grid was derived, and the final results were scaled to be representative of the original raw data. It was found that during floods the main direction of the spatial variance of the shallow groundwater monitoring wells alters, from perpendicular to the river to parallel with it for over a period of about two week. However, witht the passing of the flood, this returns to its original orientation in ~2 months. It is likely that this process is related first to the fast removal of clogged riverbed strata by the flood, then to their slower replacement. In addition, the study highlights the importance of assessing the direction of the spatial autocorrelation structure of shallow groundwater monitoring networks, especially if the aim is to derive interpolated maps for the further investigation or modeling of flow.

Proxy records of annual/decadal temperature- and hydroclimate variability from the Carpathian-Balkan Region for the past two millennia, a literature review

In the present paper a systematic compilation of temperature and moisture sensitive proxy records is presented for the Common Era of the Carpathian- Balkan region with the aim of creating a comprehensive database. It will hopefully facilitate an orientation and an overview among available literature, and hopefully serve as a valuable and solid basis for the climate research community. Authors welcome all contributions in the topic to further broaden the scope of the initiative.