Abstract
Monitoring and time-series analysis of the hydrological parameters electrical conductivity (EC), water pressure, precipitation and tide were carried out, to understand the characteristics of the parameter variations and their correlations at a coastal area in Busan, South Korea. The monitoring data were collected at a sharp interface between freshwater and saline water at the depth of 25 m below ground. Two well-logging profiles showed that seawater intrusion has largely expanded (progressed inland), and has greatly affected the groundwater quality in a coastal aquifer of tuffaceous sedimentary rock over a 9-year period. According to the time series analyses, the periodograms of the hydrological parameters present very similar trends to the power spectral densities (PSD) of the hydrological parameters. Autocorrelation functions (ACF) and partial autocorrelation functions (PACF) of the hydrological parameters were produced to evaluate their self-correlations. The ACFs of all hydrologic parameters showed very good correlation over the entire time lag, but the PACF revealed that the correlations were good only at time lag 1. Crosscorrelation functions (CCF) were used to evaluate the correlations between the hydrological parameters and the characteristics of seawater intrusion in the coastal aquifer system. The CCFs showed that EC had a close relationship with water pressure and precipitation rather than tide. The CCFs of water pressure with tide and precipitation were in inverse proportion, and the CCF of water pressure with precipitation was larger than that with tide.
Résumé
Un suivi et des analyses des séries chronologiques de paramètres hydrologiques, tels que la conductivité électrique (CE), la pression de l’eau, les précipitations et la marée ont été effectués, afin de comprendre les caractéristiques des variations des paramètres et leurs corrélations dans la zone côtière de Busan, en Corée du Sud. Les données du suivi ont été collectées au niveau de l’interface abrupte entre l’eau douce et l’eau salée à une profondeur de 25 m sous la surface du sol. Deux diagraphies en forage ont montré que l’intrusion d’eau de mer s’est largement répandue (à l’intérieur des terres), et a fortement impacté la qualité des eaux souterraines dans l’aquifère côtier constitué de roches sédimentaires tufacées au cours d’une période de 9 ans. Selon les séries chronologiques, les périodogrammes des paramètres hydrologiques montrent des tendances similaires aux densités spectrales de puissance (DSP) des paramètres hydrologiques. Les fonctions d’autocorrélation (FAC) et les fonctions d’autocorrélation partielle (FACP) des paramètres hydrologiques ont été obtenues pour évaluer leurs corrélations. Les FAC de tous les paramètres hydrologiques ont montré de très bonnes corrélations sur l’ensemble des décalages temporels, mais les FACP ont mis en évidence de bonnes corrélations uniquement pour le décalage temporel 1. Les fonctions de corrélation croisée (FCC) ont été utilisées pour évaluer les corrélations entre les paramètres hydrologiques et les caractéristiques de l’intrusion saline dans le système aquifère côtier. Les FCC ont montré que la CE est étroitement corrélée avec la pression de l’eau et les précipitations, plutôt qu’avec la marée. Les FCC de la pression de l’eau avec la marée et les précipitations sont inversement proportionnelles, et la FCC de la pression de l’eau est plus grande que celle avec la marée.
Resumen
Se realizó un monitoreo y el análisis de series de tiempo de los parámetros hidrológicos, conductividad eléctrica (EC), presión del agua, precipitación y marea, para comprender las características de las variaciones en los parámetros y sus correlaciones en una zona costera en Busan, Corea del Sur. Los datos de monitoreo se recolectaron en una nítida interfaz entre agua dulce y agua salina a una profundidad de 25 m bajo el nivel del terreno. Los registros de dos perfiles de pozos mostraron que la intrusión de agua de mar se expandió ampliamente (avanzó hacia el interior) y afectó en gran medida a la calidad del agua subterránea en un acuífero costero de rocas sedimentarias tufáceas durante un período de 9 años. Según los análisis de las series temporales, los periodogramas presentan tendencias muy similares a las densidades espectrales de potencia (DPS) de los parámetros hidrológicos. Para evaluar las autocorrelaciones de los parámetros hidrológicos se generaron las funciones de autocorrelación (ACF) y de autocorrelación parcial (PACF). Las ACF de todos los parámetros hidrológicos mostraron muy buena correlación durante todo el intervalo de tiempo, pero las PACF revelaron que las correlaciones eran buenas solo en el desfase temporal 1. Las funciones de correlación cruzada (CCF) se utilizaron para evaluar las correlaciones entre los parámetros hidrológicos y las características de la intrusión de agua de mar en el sistema acuífero costero. Las CCF mostraron que la CE tenía una estrecha relación con la presión del agua y la precipitación más que con la marea. Las CCF de la presión del agua con la marea y la precipitación fueron en proporción inversa, y las CCF de la presión del agua con la precipitación fue mayor que con la marea.
نبذة مختصرة.
تم إجراء عمليات رصد وتحليل لسلاسل المعامِلات الهيدرولوجية الزمنية: التوصيل الكهربائي (EC)، والضغط المائي، ونسبة امتصاص الأمطار، والمد والجزر لفهم التغيرات التي تطرأ على خصائص هذه المعامِلات وارتباطاتها في احدى المناطق الساحلية في بوسان بكوريا الجنوبية. وقد جُمعت بيانات الرصد في الحد الفاصل بين المياه العذبة والمالحة على عمق 25 متراً تحت سطح الأرض، حيث أظهر تسجيل القراءات في بئرين أن مياه البحر المالحة توسعت بشكل كبير (تقدمت باتجاه اليابسة)، مما أدى الى تأثيرها بصورة ملحوظة على جودة المياه الجوفية لخزان ساحلي مكون من صخور التف الرسوبية لفترة تمتد الى 9 سنين. وطبقاً لتحليل السلاسل الزمنية فان تمثيل الفترات الزمنية للمعامِلات الهيدرولوجية يُفصح عن اتجاهات متماثلة لكثافة القدرة الطيفية (PDS) لهذه المعامِلات. تم ايضاً توليد دوال الارتباط الذاتي (ACF)، ودوال الارتباط الذاتي الجزئي (PACF) للمعامِلات الهيدرولوجية بغرض التقييم الذاتي للارتباطات. وقد أظهرت دوال الارتباط الذاتي (ACF) لجميع المعامِلات الهيدرولوجية ارتباطاتٍ جيدة جداً على طول الفارق الزمني، بينما أظهرت دوال الارتباط الذاتي الجزئي (PACF) أن الارتباطات كانت جيدة في الفارق الزمني الأول فقط. تم أيضاً استخدام دوال الارتباط المتبادل (CCF) لتقييم الارتباطات بين المعامِلات الهيدرولوجية وخصائص مياه البحر المالحة التي تقدمت واخترقت الخزان الساحلي. وقد أظهرت دوال الارتباط المتبادل (CCF) أن التوصيل الكهربائي (EC) له علاقة وثيقة مع الضغط المائي ونسبة امتصاص الأمطار مقابل علاقته مع المد والجزر، وأظهرت دوال الارتباط المتبادل (CCF) للضغط المائي علاقة تناسب عكسي مع المد والجزر ونسبة امتصاص الأمطار، حيث أن دوال الارتباط المتبادل (CCF) للضغط المائي مع نسبة امتصاص الأمطار كانت أكبر منها مع المد والجزر.
সারকথা
বুসান, দক্ষিণ কোরিয়া উপকূলীয় অঞ্চলে প্যারামিটার বৈচিত্র এবং তাদের পারস্পরিক সম্পর্কের বৈশিষ্ট্যগুলি বোঝার জন্য জলবাহী প্যারামিটারের তড়িৎ পরিবাহিতা (ইসি), জল চাপ, বৃষ্টিপাত এবং জোয়ার নিরীক্ষণ এবং সময়-সিরিজ বিশ্লেষণ করা হয়েছিল। মাটির নীচের ২৫ মিটার গভীরতার মধ্যে তাজা জল এবং লবণাক্ত জল এর মধ্যে একটি ধারালো ইন্টারফেসে পর্যবেক্ষণকৃত তথ্য সংগ্রহ করা হয়েছিল। দুটি ভাল লগিং প্রোফাইলে দেখিয়েছে যে সমুদ্রপৃষ্ঠের ঘিরে ব্যাপকভাবে বিস্তৃত (অভ্যন্তরীণ প্রগতিশীল) বিস্তৃত, এবং ৯ বছরের সময়ের মধ্যে টফ্রেসিয়াস পাললিক শিলা উপকূলীয় জীবাশ্মে ভূগর্ভস্থ পানির গুণমানকে ব্যাপকভাবে প্রভাবিত করেছে। সময় সিরিজের বিশ্লেষণ অনুযায়ী, জলবিদ্যুৎ প্যারামিটারের সময়সীমার জলড্রালিয়াল প্যারামিটারগুলির বিদ্যুৎ বর্ণালী ঘনত্ব (পি এস ডি) তে খুব অনুরূপ প্রবণতা উপস্থাপন করে। স্বায়ত্তশাসন ফাংশন (এ সি এফ) এবং জলবাহী প্যারামিটারের আংশিক স্বায়ত্তশাসন ফাংশন (পি এসি এফ) তাদের আত্ম-সম্পর্কের মূল্যায়ন করতে উত্পাদিত হয়। সমস্ত হাইড্রোলজিক পরামিতিগুলির (এ সি এফ) পুরো সময়কালের মধ্যে খুব ভাল সম্পর্ক দেখিয়েছে, কিন্তু পিএসিএফ জানায় যে, সম্পর্কগুলি কেবল সময়ের ব্যবধানে ভাল ছিল ১. জল সম্পর্কীয় প্যারামিটার এবং বৈশিষ্ট্যগুলির মধ্যে পারস্পরিক সম্পর্ক নির্ণয় করার জন্য ক্রস ক্রস ক্রসনলেশন ফাংশন (সি সি এফ) ব্যবহৃত হয়েছিল উপকূলীয় জলজ প্রাণী সিস্টেমের মধ্যে সমুদ্রপৃষ্ঠের অনুপ্রবেশের। সিসিএফস দেখিয়েছে যে “ই সি” এর জোয়ার চাপের পরিবর্তে জল চাপ এবং বৃষ্টিপাতের সাথে ঘনিষ্ঠ সম্পর্ক রয়েছে। জোয়ার এবং বৃষ্টিপাতের সঙ্গে জল চাপ “সি সি এফ” বিপরীত অনুপাত ছিল, এবং বৃষ্টিপাতের সঙ্গে জল চাপ সিসিএফ জোয়ার সঙ্গে যে চেয়ে বড় ছিল।.
摘要
进行了水文参数电导率、水压、降水和潮汐监测和时序分析,目的就是了解韩国南部Busan沿海地区参数变化特征及其相关性。收集了地下25米处淡水和咸水界面的监测数据。两个录井剖面显示海水入侵大幅扩张(趋向陆地),在过去九年期间大大影响了凝灰质沉积岩沿海含水层的地下水水质。根据时序分析,水文参数周期图显示出与水文参数能谱密度非常类似的趋势。得出了水文参数自相关函数和部分自相关函数用来评估他们的自相关性。所有的水文参数自相关函数在整个时间滞后上显示出非常好的相关性,但是部分自相关函数显示相关性只有在时间滞后1上非常好。交叉相关性函数用来评估沿海含水层系统的水文参数和海水入侵特征之间的相关性。交叉相关性函数显示,电导率与水压和降水而不是潮汐有非常紧密的关系。水压与潮汐和降水的交叉相关性函数呈反比,水压与降水的交叉相关性函数比其与潮汐的交叉相关性函数要大。
सार
बुसान, दक्षिण कोरिया के तटीय इलाके में पैरामीटर विविधताओं की विशेषताओं और उनके संबंधों की विशेषताओं को समझने के लिए, जलविद्युत पैरामीटर, विद्युत चालकता (ईसी), जल दबाव, वर्षा और ज्वार की निगरानी और समय-श्रृंखला विश्लेषण किया गया। निगरानी के आंकड़े ताजे पानी और खारा पानी के बीच एक तेज अंतर पर जमीन से नीचे २५ मीटर की गहराई पर एकत्र किए गए थे। दो अच्छी तरह से लॉगिंग प्रोफाइल ने दिखाया है कि समुद्री जल घुसपैठ ने बड़े पैमाने पर विस्तार किया (अंतर्देशीय प्रगतिशील) है, और नौ साल की अवधि में तफ़सील तलछटी रॉक के तटीय जलीय जल में भूजल की गुणवत्ता को बहुत प्रभावित किया है। समय श्रृंखला के विश्लेषण के अनुसार, जल विज्ञान मापदंडों के कालक्रमों में हाइड्रोलॉजिकल मापदंडों की शक्ति वर्णक्रमीय घनत्व (पी एस डी) के लिए बहुत समान रुझान मौजूद हैं। हाइड्रॉलॉजिकल मापदंडों के आटोोकोरेरलिलेशन फ़ंक्शन (ए सी एफ) और आंशिक ऑटोोकोर्रेलेशन फ़ंक्शन (पीएसीएफ) को उनके स्वयं-सहसंबंधों का मूल्यांकन करने के लिए तैयार किया गया था। सभी हाइड्रोलोजी मापदंडों के एसीएफ पूरे समय के अंतराल पर बहुत अच्छा संबंध दिखाते हैं, लेकिन पीएसीएफ ने बताया कि सहसंबंध केवल समय के अंतराल पर अच्छा थे १. जल संबंधों के कार्यों (सी सी एफ) का उपयोग जल-संबंधी मापदंडों और विशेषताओं के बीच के संबंधों का मूल्यांकन करने के लिए किया गया था तटीय जलविस्फोट प्रणाली में समुद्री जल का घुसपैठ सीसीएफ ने दिखाया कि ईसी का पानी के दबाव के साथ घनिष्ठ संबंध था और ज्वार की बजाय वर्षा होती थी। ज्वार और वर्षा के साथ पानी के दबाव के सीसीएफ व्युत्क्रम अनुपात में थे, और वर्षा के साथ पानी के दबाव का सीसीएफ ज्वार के मुकाबले बड़ा था।.
초록
전기전도도, 수압, 강수량 및 조석 등의 수문인자에 대한 모니터링과 시계열분석이 대한민국 부산의 해안지역에서 그 인자들의 변동특성과 상관성을 파악하기 위하여 수행되었다. 관측 자료는 해수와 담수의 경계면이 위치하는 25 m 심도에서 수집되었다. 2개의 지하수공 검층 자료에 의하면 9년 동안에 해수침투가 크게 확장되어 응회암질 퇴적암 대수층내의 해안 지하수 수질에 크게 영향을 주었다. 시계열자료 분석에 의하면, 수문인자들의 주기도는 파우어스펙트럭밀도(PSD)와 매우 유사하다. 수문인자들의 자기상관함수(ACF)와 편자기상관함수(PACF)가 자기유사성을 평가하기 위하여 만들어졌는 데, 모든 수문자료의 자기상관함수는 전 시차에서 매우 좋은 상관성을 나타내었으나, 편자기함수는 시차 1에서만 좋은 상관성을 나타내었다. 교차상관함수(CCF)가 또한 수문인자와 해안대수층에 대한 해수침투와의 상관성을 파악하기 위하여 이용되었다. 교차상관함수에 의하면 전기전도도는 조석보다는 수압과 강수량에 밀접한 관련이 있다. 수압과 조석 및 강수량과의 관계는 역의 상관성이 있으며, 수압은 조석보다는 강수량에 상관성이 더 큰 것으로 나타났다.
Resumo
Monitoramento e análise de series temporais dos parâmetros hidrológicos condutividade elétrica (CE), pressão da água, precipitação e marés foram conduzidos para entender as características da variação dos parâmetros e suas correlações em uma área costeira em Busan, Coréia do Sul. Os dados de monitoramento foram coletados na superfície abrupta entre as águas doces e as águas salinas a uma profundidade de 25 m abaixo da superfície. Dois perfis geofísicos de poços mostraram que a intrusão de água do mar foi largamente expandida (progressão ao continente), e afetou amplamente a qualidade das águas subterrâneas em um aquífero costeiro de rocha sedimentar tufosa ao longo de um período de 9 anos. De acordo com a análise de séries temporais, os periodogramas dos parâmetros hidrológicos apresentaram tendências muito similares às densidades espectrais (PSD) dos parâmetros hidrológicos. Funções de autocorrelação (FAC) e funções de autocorrelação parciais (FACP) dos parâmetros hidrológicos foram produzidas para avaliar as próprias correlações. As FAC de todos os parâmetros hidrológicos mostraram uma correlação muito boa em todo o intervalo de tempo, mas as FACP revelaram que as correlações eram boas apenas no intervalo de tempo 1. As funções de correlação cruzada (FCC) foram utilizadas para avaliar as correlações entre os parâmetros hidrológicos e as características de intrusão de água do mar no sistema aquífero costeiro. As FCC mostraram que a CE teve uma relação estreita com a pressão da água e a precipitação ao invés da maré. As FCC da pressão da água com maré e precipitação estavam em proporção inversa, e a FCC da pressão da água com precipitação foi maior que o da maré.
Özet
Güney Kore, Busan sahilindeki bir alanda, parametre değişkenliklerinin ve bunların korelasyonlarının özelliklerini anlamak için, elektrik iletkenliği (EC), su basıncı, yağış ve gelgit gibi hidrolojik parametreler izlenmiş ve zaman serileri analizi gerçekleştirilmiştir. İzleme verileri, tatlı su ile tuzlu su arasındaki keskin bir ara yüzden ve yüzeyden 25 m derinlikten toplanmıştır. İki kuyu logu profili, deniz suyu girişiminin büyük oranda genişlediğini (kıyı içine ilerlediğini) ve dokuz yıllık bir süre içinde tüflü sedimanter kayadan oluşan kıyı akiferinde, yeraltı sularının kalitesini büyük ölçüde etkilediğini göstermiştir. Zaman serileri analizlerine göre, hidrolojik parametrelerin periyodogramları, hidrolojik parametrelerin güç spektral yoğunluğuna (PSD) çok benzer trendler sunmaktadır. Öz-korelasyonlarını değerlendirmek için, hidrolojik parametrelerin otokorelasyon fonksiyonları (ACF) ve kısmi otokorelasyon fonksiyonları (PACF) üretilmiştir. Bütün hidrolojik parametrelerin ACF’leri, tüm gecikme (lag) süresi boyunca çok iyi korelasyon göstermiş; ancak PACF, korelasyonların sadece lag 1’de iyi olduğunu ortaya koymuştur. Hidrolojik parametreler ve kıyı akifer sisteminde görülen deniz suyu girişiminin özellikleri arasındaki korelasyonları değerlendirmek için çapraz korelasyon fonksiyonları (CCF) kullanılmıştır. CCF’ler, EC’nin gelgitten ziyade, su basıncı ve yağış ile yakın ilişkili olduğunu göstermiştir. Su basıncı ile gelgit ve yağışın CCF’lerinin ters orantılı olduğu, su basıncı ile yağışın CCF’sinin ise, su basıncı ile gelgitin CCF’sinden daha büyük olduğu belirlenmiştir.
Trừu tượng
Theo dõi và phân tích chuỗi thời gian của các thông số thuỷ văn dẫn điện, áp suất nước, lượng mưa và thủy triều đã được thực hiện, để hiểu được đặc điểm của các biến số, tham số và tương quan của chúng tại các khu vực ven biển ở Busan, Hàn Quốc. Các dữ liệu giám sát được thu thập ở một điểm tiếp xúc giữa nước ngọt và nước mặn ở độ sâu 25 m dưới mặt đất. Hai hồ sơ cho thấy sự xâm nhập của nước biển đã được mở rộng (đã tiến triển trong nội địa) và đã ảnh hưởng lớn đến chất lượng nước ngầm trong một bể chứa đá trầm tích thạch anh trong 9 năm. Theo phân tích chuỗi thời gian, các khoảng thời gian của các thông số thuỷ văn có xu hướng rất giống với mật độ phổ công suất (PSD) của các tham số thuỷ văn. Các chức năng tự tương quan (ACF) và các chức năng tự tương quan một phần (PACF) của các thông số thuỷ văn đã được tạo ra để đánh giá sự tương quan của chúng. ACFs của tất cả các thông sốthuỷ văn cho thấy mối tương quan rất tốt trong suốt thời gian trễ, nhưng PACF cho thấy tương quan chỉ tốt ở thời gian trễ 1. Các chức năng tương quan chéo (CCF) được sử dụng để đánh giá mối tương quan giữa các tham số thuỷ văn và các đặc tính xâm nhập của nước biển trong hệ thống tầng nước ngầm ven biển. Các CCFs cho thấy EC đã có mối quan hệ chặt chẽ với áp suất nước và lượng mưa hơn là thủy triều. Các CCF của áp suất nước với thủy triều và lượng mưa có tỷ lệ ngược, và CCF của áp suất nước với lượng mưa lớn hơn so với thủy triều.
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Introduction
Effective management of freshwater reservoirs is very important for the sustainability of natural resources. Freshwater stored in coastal aquifers is particularly vulnerable in terms of water quality degradation due to its proximity to seawater, in combination with the intensive water demands that accompany the higher population densities of coastal zones. The water level in an aquifer is an important parameter in groundwater hydrology, and a careful and detailed analysis of its variation in time and space reveals useful information on the aquifer system behavior (Aflatooni and Mardaneh 2011). Various factors affecting the groundwater level are groundwater pumping, recharge, precipitation, water pressure, evapo-transpiration, interaction with surface-water bodies, and the tidal oscillation of the sea level in coastal aquifers (Ataie-Ashtiani et al. 1999; Maréchal et al. 2002). The pressure of tidal waves causes periodic fluctuation of the groundwater level in the coastal aquifer. This damping effect progressively diminishes the amplitude of groundwater head in the inland direction (Maréchal et al. 2002). The monitoring of primary hydrological parameters (water pressure, precipitation, electrical conductivity and tide) takes into account the principal sources of information on the seawater intrusion against the coastal aquifer groundwater system. (Winter et al. 2000; Moon et al. 2004; Ahmadi and Sedghamiz 2007; Christophe et al. 2016).
Hydrological processes are usually nonlinear, complex, dynamic, and widely scattered due to the influence of physical processes involving variability in space and time. Further complexity is added when such processes are observed at small spatiotemporal scales, but estimates are needed for very large ones; therefore, it is vital to evaluate whether these processes have different behaviors at different scales. These processes and properties vary at different spatiotemporal scales, and their variations essentially affect groundwater level and quality fluctuations in coastal aquifer systems. Time series of groundwater parameters usually exhibit complex fluctuations owing to the interactions of many factors, and time series analysis has been widely used in the evaluation and forecast of groundwater monitoring data, because it elucidates the characteristics of these complicated features. Many research projects decompose groundwater-level variations into trend, periodicity and random components, and combine the components together as a model to forecast the future variations (Hu et al. 2001; Kim et al. 2005, 2007; Zhao et al. 2007; Zhou et al. 2007; Yang et al. 2009; Chung et al. 2015).
The permeation of seawater through coastal shores and eventual intrusion into coastal aquifers affects the salinity levels of the groundwater. The degree of seawater intrusion varies with the water pressure, precipitation and tidal fluctuations. Time series analysis can gain insight into the relationship between seawater intrusion and groundwater parameters. In this study, the freshwater–saltwater interface was considered as a sharp interface, and a TLC meter was installed at 25-m depth in a monitoring well to observe the interface (Fig. 1). The TLC device measured temperature (T), groundwater level (L) and electrical conductivity (C) of the groundwater. Spectral analysis methods outlined by Shumway and Stoffer (2011) were used to understand the fluctuation behavior of selected hydrological parameters.
The purpose of this study is to understand the variation of the hydrological parameters EC, water pressure, precipitation and tide, and their correlations at a coastal area in Busan, South Korea, using monitoring techniques and time series analysis of these hydrological parameters. Prediction of the extent and influence of seawater intrusion is possible for the long period covered through this study.
Materials and methods
Study area and field measurements
The study area (Fig. 2) is in the Nam-gu District in Busan City, and includes Pukyong National University Campus and the surrounding coastal area. The geology of the study area is mainly composed of tuffaceous sedimentary rocks and andesitic volcanic breccia. The geological time of the rocks is the Cretaceous Period of the Mesozoic Era. Groundwater in the study area is relatively vulnerable to seawater intrusion, because the coast is composed of a sandy beach and reclaimed land.
The study area has four climatological seasons, and received 1,222 and 1,773 mm of precipitation in 2000 and 2009, respectively. The precipitation of 2000 was much smaller than that of 2009 because of drought. Most of the precipitation falls from May to September, with averages 963.5 and 1,352.2 mm in 2000 and 2009, respectively (Fig. 3a,b). During summer, a typhoon usually comes to the Korean Peninsula, accompanied by heavy rain.
Water level and EC were measured at a monitoring well at Pukyong National University from August 2009 to October 2009, using an automatic TLC sensor with a time interval of 5 min. The monitoring period covered a short dry season (see Fig. 3 precipitation data). The reason for gathering hydrogeological data in the dry season is to reduce the rainfall effect on the groundwater level and quality data. The hydrological data in the dry season was monitored because groundwater quality was not much influenced by rainfall. This well is developed in an unconfined aquifer, and is located 650 m from the coastline. It is 120 m in depth, and its topographic elevation is 4.1 m above mean sea level. The early water level was about 3.9 m below the ground surface in 2009. In this area, the aquifer is almost homogeneous and consists of tuffaceous sedimentary rocks.
The freshwater–saline water interface was measured at the depth of about 25 m below ground surface (−GL). The interface between the freshwater and saline water was considered as a sharp interface. The TLC meter (model 107) made by Solinst Canada Ltd. was used to collect data and was installed at 25 m (−GL). Tide was monitored by the Korea Hydrographic and Oceanographic Administration, and precipitation was measured by the Korea Metrological Administration.
Time series analyses
Time series models have been developed for various hydrologic and environmental applications for effectively forecasting risk (Li et al. 2009; Xu et al. 2009; Erdogan and Gulal 2009). A time series can be composed of a case observed at discrete times, averaged over a time interval, or recorded continuously with time. A sequence of observations made in a time series can be influenced by three components: (1) a trend or long-term component, (2) a cyclical or oscillating component and (3) a random or irregular component. Several techniques are available for separating the trend component from the oscillating fluctuations and random variations in a time series. An important aspect of hydrogeological studies is the determination of long- and short-term trends, which can show the effect of all processes that influence the aquifer over a long and short period (Box and Jenkins 1976).
A short overview of periodogram, spectral density function, auto and partial auto correlation analysis (ACF and PACF) and cross correlation functions (CCF) is presented. The mathematical expressions of the functions are shown in detail by Jenkins and Watts (1968), Mangin (1984), Box et al. (1994), Padilla et al. (1994) and Laroque et al. (1998). The simple auto-correlation analysis quantifies the linear dependency of successive values over a time period. The auto-correlation function, ρ(k) is expressed as
where k is the time lag (k = 0 to m) for which m is the cut point, n is the number of events, xt is a single event at time t, and \( \overline{X} \) is the mean of events. C(k) is an auto-covariance of time series data, x(t). The cutting point is usually determined based on the interval of the analysis and the given circumstance. If the time series has strong interdependency and a long memory effect, the auto-correlation function shows a gently decreasing slope and nonzero values over a long time lag. However, if the time series is uncorrelated such as for rainfall, the auto-correlation function decreases very quickly and reaches a zero value in a short time (Lee and Lee 2000; Liang 2011; Chung et al. 2015).
The partial autocorrelation function (PACF) of a stationary process, xt, denoted Øhh, for h = 1, 2, …, (where h is the separation between xt + h and xt) is
and
Both \( \left({x}_{t+h}-{\widehat{x}}_{t+h}\right) \) and \( \left({x}_t-{\widehat{x}}_t\right) \) are uncorrelated with {xt + 1, …, xt + h − 1}. The PACF, Øhh, is the correlation between xt + h and xt with the linear dependence of {xt + 1, …, xt + h − 1} on each, removed (Shumway and Stoffer 2011). If the process xt is Gaussian, then Øhh = corr(xt + h, xt ⃓ xt + 1, …, xt + h − 1); that is, Øhh is the correlation coefficient between xt + h and xt in the bivariate distribution of (xt + h, xt) conditional on {xt + 1, …, xt + h − 1}.
ACF is not as useful in the identification of the order of an auto-regressive process (AR) for which it will most likely have a mixture of exponential decay and damped sinusoidal expressions. PACF is useful for the analysis of the time series with the AR structure (Montgomery et al. 2008). The simple spectral density analysis is complementary to the auto-correlation analysis. The spectral density function corresponds to change from a time mode to a frequency mode through a Fourier transformation of the auto-correlation function. The Blackman and Turkey (1958) method was used for the power spectral density (PSD) in this study. The method corresponds to change from a time mode to a frequency mode through a complex Fourier transformation of the auto-correlation function. The actual computation of the power spectrum can only be performed at a finite number of different frequencies by employing the Fast Fourier Transformation (FFT; Trauth 2015). The FFT is a method of computing a discrete Fourier transform with reduced execution time.
where fsis sampling frequency, M is maximum lag, Xx(f) is a complex Fourier transformation of the auto-correlation function, and PSDx(f) is power spectral density.
The cross-correlation analysis is used to establish a link between the input time series and the output time series. If the input time series is random, the cross-correlation function, rxy(k), corresponds to the impulse response of the system. In other cases, the cross-correlation function provides information on the interrelationship between the input and the output time series data as well as the importance of these relationships. The definition of a cross-correlation coefficient is as follows:
where Cxy(k) is the cross-covariance of x(t) and y(t) time series, and σx, σy are the standard deviations of two time-series, respectively. The time series analyses were performed by SPSS (Ver. 21).
Results and discussion
Variations of water pressure and EC at the interface between freshwater and saline water
Figure 4a,b illustrate the EC variations with depth in the monitoring well in June 2000 and August 2009, respectively. At the beginning of the well development in June 2000, EC increased with depth at three intervals, i.e., from 22 to 79 m, from 79 to 101 m, and from 117 to 120 m (Fig. 4a). Thus, three transition zones were formed by seawater intrusion at that time. However, the transition zones changed into a saline water zone due to the complete mixing of groundwater with seawater in August 2009 (Fig. 4b). The EC value was 47,000 μS/cm below the interface in 2009, and it was nearly seawater quality. Then, the interface between freshwater and sea water was located only at 25 m depth (−GL).
Figure 5a,b show the variation of water pressure and EC with precipitation and tide at the interface at 25 m (−GL). The minimum, maximum and average values of measured parameters are presented in Table 1. The water pressure varied from 20.96 to 21.28 m at the fresh–saline water interface, and formed a quite complex shape due to the several kinds of influences such as tide, air pressure and precipitation. EC varied from 1,258 to 3,149 μS/cm, and showed a very smooth variation. EC was largely affected by precipitation rather than by tide. This was examined by the relation of precipitation with EC from 22 August 2009 to 17 October 2009 (Fig. 5a,b). EC began to decrease due to the increase of precipitation at the beginning of October 2009.
If the water pressure at the fresh-saline water interface was increased, EC decreased due to the increase of freshwater, and vice versa. When water pressure was increased at the end of August 2009, EC decreased due to the increase of freshwater. When water pressure decreased during September 2009, EC increased due to the decrease of freshwater. Figure 5b shows the relation of water pressure and EC with tide. Water pressure was influenced by tidal variation. Water pressure generally increased according to the rise of tide, and in case of the fall of tide, water pressure decreased. EC is decreased by the increase of water pressure, and vice versa; thus, the level and quality of groundwater were affected by seawater intrusion in the study area.
Periodograms and spectral density functions (SDF)
The periodograms of hydrological parameters according to frequency and period are given in Fig. 6. All periodograms of the frequency domain are in inverse proportion to those of the period domain, because frequency is inversely proportional to period. The periodogram of tide is similar to that of precipitation on the basis of frequency, but the periodogram of tide is different from that of precipitation on the basis of period. Tide has a big periodogram value on the very low frequency, and many small periodogram values on the higher frequencies. Tide has a big periodogram value at the period of less than 5 × 103. Precipitation also has a big periodogram value on the very low frequency; however, its periodogram value on the period domain continuously increases and ends as a big value. Water pressure and EC also have high periodogram values at the very low frequency, but their periodogram values are different on the period domain. Water pressure has very low periodogram values until the period of 5 × 103, and it increases after that period value. The periodogram value of EC increases continuously.
Spectral density functions (SDF) of selected hydrological parameters such as EC, water pressure, precipitation and tide are shown in Fig. 7. The SDF was calculated using the Blackman-Turkey method. This method used the complex Fourier transformation for the autocorrelation functions of time series data. The spectral density functions of hydrologic parameters are quite similar to the periodograms of hydrologic parameters in this study. The behaviors of spectral density functions of hydrologic parameters are also similar to each other, and their highest peaks have a single point on the very small frequency. The spectral density function of EC shows the similar trend as those of tide, precipitation and water pressure on both the frequency and period domains. This suggests that EC fluctuations were affected by tide, water pressure and precipitation (Diggle 1992; Lu et al. 2014). All hydrological parameters show quite similar spectra with an initial break in slope and gradual fall-off until the increased asymptotic frequency. To explain the variation in frequency and period, additional factors must play controlling roles. This behavior suggests the preponderance of long memory in the interaction between groundwater and seawater. The results of these analyses show that hydrological parameters are useful for predicting the seawater intrusion in the monitoring well.
Autocorrelation and partial autocorrelation functions (ACF and PACF)
Figure 8 shows the ACF and PACF of the hydrological parameters EC, water pressure, precipitation and tide. The ACFs and PACFs of precipitation and EC present nearly the same pattern. The ACFs almost approach 1.0 regardless of the number of the time lag; however, the PACFs are 1.0 only at the time lag 1, and almost 0 at more than the time lag 1. The ACF of tide gradually goes down according to the increase of the time lag, and approaches 0.75. The PACF of tide is 1.0 only at the time lag 1, and its absolute value is decreased to 0 with the increasing time lag number. The ACF of water pressure is 1.0 regardless of the number of time lag, but the PACF of water pressure is gradually decreased to 0 with the increasing time lag number. The ACFs of all the hydrological parameters show very good correlations over the entire time lag; however, the PACFs of precipitation and EC reveal good correlations only at time lag 1, and they are almost 0 over the rest of the time lags. The PACFs of tide and water pressure show good correlations only at time lag 1, and their correlations decrease with the increasing time lag number; thus, the PACF cuts off after the first time lag, and the only significant sample PACF value is at time lag 1, suggesting that for the first-order autoregressive process, the AR(1) model is indeed appropriate to the hydrologic data (Montgomery et al. 2008). The ACF and PACF of hydrological data are effective analyses for forecasting seawater intrusion against groundwater in the coastal area (Tularam and Keeler 2006).
Cross correlation functions (CCF)
The CCF was used to evaluate the correlations between the hydrological parameters EC, water pressure, precipitation and tide, and the characteristics of seawater intrusion in a coastal aquifer system. In this analysis, EC and water pressure were the objects of cross correlation using tide, precipitation and water pressure. Figure 9 presents the graphs of CCFs for these hydrological parameters.
The cross correlation between EC and tide was −0.024 to –0.026 (Fig. 9a), and the correlation was largely increased to −0.063 to −0.065 after the natural log transformation of tide data (Fig. 9b). The cross correlation between EC and precipitation was 0.316 to 0.317 (Fig. 9c) and it suggests that EC was largely affected by precipitation rather than tide. The cross correlation between EC and water pressure was −0.190 to −0.195 (Fig. 9d), and their relation was in inverse proportion. This means that the increase of water pressure decreased the EC, because the increase of water pressure resulted from the increase of freshwater. EC generally has a close relationship with water pressure or precipitation; however, their cross correlation coefficients were not large in this study, because the amount of data was not enough for the definite identification of their relations. The cross correlation between water pressure and tide was −0.049 to −0.089 (Fig. 9e), and that between water pressure and precipitation was −0.234 to −0.241 (Fig. 9f); thus, water pressure was much more influenced by precipitation than tide. The variation of water pressure was partially caused by precipitation events acting as a recharge source (Namdar Ghanbari and Bravo 2011). From the cross correlations between the hydrologic parameters, it is understood that EC was much more influenced by precipitation, and water pressure was also much affected by precipitation in the study area.
Conclusions
The transition zone between fresh and saline water was changed into a saline water zone due to the complete mixing of groundwater with seawater in the monitoring well after 9 years of well development. The interface existed only at 25 m depth in August 2009, although it was located at 22, 79, 101 and 117 depths at the time of well development in 2000. Moreover, EC greatly increased from 30,000 to 47,000 μS/cm over the 9-year period; thus, seawater intrusion expanded widely during the 9 years of study and greatly affected the groundwater quality in this coastal aquifer of tuffaceous sedimentary rock.
EC and water pressure were compared to the variations of precipitation and tide. EC was largely affected by water pressure and precipitation, rather than tide. Water pressure was influenced by precipitation as well as tide. The periodograms of hydrological parameters were produced on the basis of frequency and period. All periodograms on the frequency domain were in inverse proportion to those on the period domain. The periodograms of all hydrological parameters were quite similar to each other, and had a big periodogram value on the very low frequency. The power spectral density (PSD) of selected hydrological parameters such as EC, water pressure, precipitation and tide were produced by the Blackman-Turkey method, and were nearly the same as the periodograms of the hydrologic parameters used in this study. This behavior highlights the significance of long-term behavior in the interaction between groundwater and seawater.
The ACF and PACF of the hydrological parameters were produced to understand their self-correlations. The ACFs of all hydrologic parameters showed very good correlation over the entire time lag, but the PACFs revealed that their correlations were good only at time lag 1. The CCF was used to evaluate the correlations between the hydrological parameters and the characteristics of seawater intrusion in the coastal aquifer system. The large cross correlation between EC and precipitation suggests that EC was largely affected by precipitation rather than tide. The inverse cross correlation between EC and water pressure means that the increase of water pressure decreased the EC, because the increase of water pressure resulted from the increase of freshwater. From the CCFs between hydrologic parameters, it is understood that EC was much influenced by precipitation, and water pressure was also much affected by precipitation in the study area. The monitoring and time series analysis of hydrological parameters such as water pressure, EC, precipitation and tide have been found to be very useful to understand the characteristics of the parameter variations and their correlations, and the extent and influence of seawater intrusion. The continuous monitoring of hydrological parameters will be very useful for preventing the further deterioration of groundwater quality in the coastal regions.
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Acknowledgements
We express a deep gratitude to the fruitful comments of an anonymous reviewer.
Funding
This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2016R1D1A3B03934558).
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Chung, S.Y., Senapathi, V., Sekar, S. et al. Time series analyses of hydrological parameter variations and their correlations at a coastal area in Busan, South Korea. Hydrogeol J 26, 1875–1885 (2018). https://doi.org/10.1007/s10040-018-1739-9
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DOI: https://doi.org/10.1007/s10040-018-1739-9