臺灣博碩士論文加值系統

地下水位之預測對於水資源之有效管理乃必要的，有物理架構之數值模式，需要許多含水層之水文地質特性以及適當的邊界條件，因而創造出許多不確定性。不需物理架構之黑盒分析，如機器學習、
人工智慧等，又令人無法解構模擬過程內部的機制。本研究提出兩者折衷之灰盒分析，以線性水筒模式作為地下水含水層之物理架構，建立三層水筒分別代表1)地表，2)未飽和層，及3)飽和含水層，各別有其質量守恆之水文方程式。考慮降雨補注，人為抽水，潮汐現象，以及上游監測站之來流。降雨補注與人為抽水乃基本模組(Module 1)，模組2增加了潮汐的效應，模組3乃由模組1增加了上游來流，模組4則是潮汐與上游來流皆加到基本模組中。平均抽水量(AMP)及平均潮汐影响(AMP)乃由已發表之訊號分析技術獲得。以濁水溪沖積扇第一層含水層，2015年8月1日至2018年1月1日之兩年半，每小時地下水水位及每小時雨量作為探討之數據區間。比較四種模組之預測效果。模擬成果顯示AMP 及AMT 乃有用之工具。AMP 僅利用地下水時水位資料便能補足監測井週圍抽水井之影響。AMT 則能改善沿海測站水位數據受潮汐之影响。當與上游測站之地下水水位有一致上下之相關性時，則增加上游流量之考量必能提昇模組預測準確性。

Prediction of groundwater levels is essential for effective water resource management, environmental management, infrastructure planning, and risk management. Several methods have been used for groundwater levels prediction such as white box models (physical models and numerical models) and black box approaches (data driven) such as machine learning. Both white box models and black box approaches have their limitation and shortcoming. Balancing these trade-offs is crucial for developing accurate and useful groundwater level predictions. This study introduced a grey box approach to bridge the gap between white box and black box models by building a module that describes the groundwater system as a series of three tank linearly interconnected, by only using data from monitoring wells and rain gauges. The idea was inspired by the concept of tank model, which was initially designed for rainfall-runoff simulation. The number of tanks was fix to three according to groundwater structure that is mainly divided into three main components which are surface, unsaturated zone, and saturated zone also known as groundwater aquifer. Thereby, governing equations based on mass balance were derived to describe the groundwater dynamics. This study considers components including rainfall recharge, artificial pumping, tides, and upstream discharge as the major fluxes
affecting the groundwater-level fluctuations. Since estimation of total volume pumped by human activities is challenging in an area with large number of pumping wells, this study introduced a signal processing approach to estimate the Average Magnitude of Pumping (AMP) surrounding a monitoring well. Similarly, the Average Magnitude of Tides (AMT) was also estimated. Four modules were developed in this study, and compared with each other. The basic framework (module 1) only includes AMP. In module 2 AMT was added to the basic framework, while GROUNDWATER LEVEL PREDICTION USING GREY BOX MODEL FOR AN ALLUVIAL FAN IN TAIWAN
in module 3 upstream discharge was added. Finally in module 4, AMT and upstream discharge are both added to the basic framework. All modules were applied to the first aquifer of Chou-Shui Chi alluvial fan in the central Taiwan, using data from August 1, 2015 to January 1, 2018. The groundwater levels were predicted based on these modules. Firstly, the results showed that AMP and AMT are useful tools to overcome lack information related to artificial pumping and tide effects on the groundwater level fluctuation. Secondly, the four modules performed good groundwater level predictions. Module 1 perform less accurately in the coastal area due to the absence of tidal effect in its formulation, while module 2 overcomes this missing piece. By adding the upstream discharge to the basic framework, the performance of module 3 improved for cases with good correlation between a monitoring well and its upstream station.
Then, combining upstream discharge and tide effects improved the performance of groundwater level prediction. Finally, this study highlighted the importance of analyzing the essential portion of fluxes affecting the groundwater level fluctuation.

DEDICATIONS....................................................................... I
ACKNOWLEDGEMENTS................................................................. II
摘　　要......................................................................... IV
ABSTRACT.......................................................................... V
TABLE OF CONTENTS............................................................... VII
TABLES OF FIGURES............................................................... IX
LIST OF TABLES.................................................................. XI
LIST OF SYMBOLS................................................................. XII
CHAPTER 1: INTRODUCTION........................................................... 1
1.1. IMPORTANCE OF GROUNDWATER AND GROUNDWATER ISSUES............................. 1
1.1.1. Importance of groundwater.................................................. 1
1.1.2. Groundwater issues......................................................... 1
1.1.3. Summary.................................................................... 1
1.2. GROUNDWATER MANAGEMENT....................................................... 2
1.3. GROUNDWATER LEVEL PREDICTION METHODS......................................... 2
1.3.1. Physical models............................................................ 2
1.3.2. Numerical models......................................................... 2
1.3.3. Data driven approach....................................................... 3
1.4. STUDY JUSTIFICATION AND PURPOSE.............................................. 3
1.4.1. Study justification....................................................... 3
1.4.2. Study purpose............................................................. 4
1.5. THESIS STRUCTURE............................................................. 4
CHAPTER 2: THEORETICAL FRAMEWORK.................................................. 6
2.1. GROUNDWATER SYSTEM........................................................... 6
2.2. TANK MODEL................................................................... 6
2.3. SHORT TIME FOURIER TRANSFORM (STFT).......................................... 8
2.4. LEAST SQUARE CURVE FITTING................................................... 9
2.5. PERFORMANCE METRICS.......................................................... 9
CHAPTER 3: METHODOLOGY........................................................... 11
3.1. STUDY AREA.................................................................. 11
3.2. DATA COLLECTION AND PREPARATION............................................. 11
3.3. FREQUENCY ANALYSIS.......................................................... 13
3.4. AVERAGE MAGNITUDE OF PUMPING (AMP).......................................... 15
3.5. AVERAGE MAGNITUDE OF TIDES (AMT)............................................ 15
3.6. CONCEPTUAL GROUNDWATER SYSTEM DEVELOPMENT................................... 16
3.6.1. Module 1: basic model.................................................... 17
3.6.2. Module 2: with tides..................................................... 17
3.6.3. Module 3: with upstream discharge........................................ 18
3.6.4. Module 4: with both tides and upstream discharge......................... 20
3.7. GROUNDWATER LEVEL PREDICTION................................................ 20
CHAPTER 4: RESULTS AND DISCUSSION................................................ 22
4.1. AMP......................................................................... 22
4.2. AMT......................................................................... 24
4.3. RESULTS AND DISCUSSION OF THE MODULES COMPARISON............................ 25
4.3.1. Module 1: basic model.................................................... 27
4.3.2. Module 2: with tides..................................................... 28
4.3.3. Module 3: with upstream discharge........................................ 30
4.3.4. Module 4: With upstream discharge and tides.............................. 31
4.3.5. Summary.................................................................. 34
CHAPTER 5: CONCLUSION............................................................ 35
REFERENCES....................................................................... 37
APPENDIX......................................................................... 40

Ahlfeld, D. P., Mulvey, J. M., Pinder, G. F., andWood, E. F. (1988).“Contaminated groundwater remediation design using simulation, optimization, and sensitivity theory: 1. Model development.” Water Resources Research, 24(3), 431–441.
Chang, F. J., Chang, L. C., Huang, C. W., andKao, I. F. (2016).“Prediction of monthly regional groundwater levels through hybrid soft-computing techniques.” Journal of Hydrology.
Chebaane, M., El-Naser, H., Fitch, J., Hijazi, A., andJabbarin, A. (2004).“Participatory groundwater management in Jordan: development and analysis of options. Groundwater: from development to management.” Hydrogeol J, 12(1), 14–32.
Chen, C. H., Wang, C. H., Hsu, Y. J., Yu, S. B., andKuo, L. C. (2010).“Correlation between groundwater level and altitude variations in land subsidence area of the Choshuichi Alluvial Fan, Taiwan.” Engineering Geology, Elsevier B.V., 115(1–2), 122–131.
Chiu, Y. C., Sun, N. Z., Nishikawa, T., andYeh, W. W. G. (2009).“Development of an objective-oriented groundwater model for conjunctive-use planning of surface water and groundwater.” Water Resources Research, 45(12), 1–13.
Cui, Z. D., andJia, Y. J. (2018).“Physical Model Test of Layered Soil Subsidence Considering Dual Effects of Building Load and Groundwater Withdrawal.” Arabian Journal for Science and Engineering, Springer Verlag, 43(4), 1721–1734.
Durak, L., andArikan, O. (2003).“Short-time Fourier transform: Two fundamental properties and an optimal implementation.” IEEE Transactions on Signal Processing, 51(5), 1231–1242.
Fitts, C. R. (2013).Principles of Flow. Groundwater Science.
Gaur, S., Chahar, B. R., andGraillot, D. (2011).“Combined use of groundwater modeling and potential zone analysis for management of groundwater.” International Journal of Applied Earth Observation and Geoinformation, Elsevier B.V., 13(1), 127–139.
Harbaugh, A. W., Banta, E. R., Hill, M. C., andMcDonald, M. G. (2000).MODFLOW-2000, THE U.S GEOLOGICAL SURVEY MODULAR GROUND-WATER MODEL-USER GUIDE TO MODULARIZATION CONCEPTS AND THE GROUND-WATER FLOW PROCESS.
Hodson, T. O. (2022).“Root-mean-square error (RMSE) or mean absolute error (MAE): when to use them or not.” Geoscientific Model Development, Copernicus GmbH, 15(14), 5481–5487.
Hsiao, C. T., Chang, L. C., Tsai, J. P., andChen, Y. C. (2017).“Features of spatiotemporal groundwater head variation using independent component analysis.” Journal of Hydrology, Elsevier B.V., 547, 623–637.
Hsu, N. S., Chiang, C. J., Wang, C. H., Liu, C. W., Huang, C. L., andLiu, H. J. (2013).“Estimation of pumpage and recharge in alluvial fan topography under multiple irrigation practices.” Journal of Hydrology, 479, 35–50.
Hsu, S. K. (1998).“Plan for a groundwater monitoring network in Taiwan.” Hydrogeology Journal, 6(3), 405–415.
Hung, W. C., Hwang, C., Liou, J. C., Lin, Y. S., andYang, H. L. (2012).“Modeling aquifer-system compaction and predicting land subsidence in central Taiwan.” Engineering Geology, Elsevier B.V., 147–148, 78–90.
Jaeger, B. (2006).“The method of least squares.” Handbook of Research on Informatics in Healthcare and Biomedicine.
Kusiak, A. (2009).“Innovation: A data-driven approach.” International Journal of Production Economics, Elsevier, 122(1), 440–448.
Lee, J. W., Chegal, S. D., andLee, S. O. (2020).“A review of tank model and its applicability to various korean catchment conditions.” Water (Switzerland).
DeLevie, R. (2000).“Curve fitting with least squares.” Critical Reviews in Analytical Chemistry, 30(1), 59–74.
Liu, C. W. (2004).“Decision support system for managing ground water resources in the Choushui River alluvial in Taiwan.” Journal of the American Water Resources Association.
Liu, H. J., Hsu, N. S., andYeh, W. W. G. (2015).“Independent component analysis for characterization and quantification of regional groundwater pumping.” Journal of Hydrology, Elsevier B.V., 527, 505–516.
Luczaj, J. (2016).“Groundwater Quantity and Quality.” Resources 2016, Vol. 5, Page 10, Multidisciplinary Digital Publishing Institute, 5(1), 10.
Luczaj, J., andMasarik, K. (2015).“Groundwater quantity and quality issues in a water-rich region: Examples from Wisconsin, USA.” Resources, MDPI AG, 4(2), 323–357.
McMillan, T. C., Rau, G. C., Timms, W. A., andAndersen, M. S. (2019).“Utilizing the Impact of Earth and Atmospheric Tides on Groundwater Systems: A Review Reveals the Future Potential.” Reviews of Geophysics.
Megdal, S. B. (2018).“Invisible water: the importance of good groundwater governance and management.” npj Clean Water 2018 1:1, Nature Publishing Group, 1(1), 1–5.
Megdal, S. B., Gerlak, A. K., Varady, R. G., andHuang, L. Y. (2015).“Groundwater governance in the United States: common priorities and challenges.” Groundwater, Blackwell Publishing Ltd, 53(5), 677–684.
Ouédraogo, A. R., Hsu, S. M., andWang, Y. (2023).“Estimating the Average Magnitude of Pumping Surrounding Monitoring Wells Using Signal Processing.” Journal of Hydrologic Engineering, American Society of Civil Engineers, 28(4), 05023002.
Phuong, H. T., Tien, N. X., Chikamori, H., andOkubo, K. (2018).“A hydrological tank model assessing historical runoff variation in the Hieu River Basin.” Asian Journal of Water, Environment and Pollution, 15(1), 75–86.
Pitchforth, D. J., Rogers, T. J., Tygesen, U. T., andCross, E. J. (2021).“Grey-box models for wave loading prediction.” Mechanical Systems and Signal Processing, Academic Press, 159, 107741.
Qureshi, A. S., McCornick, P. G., Sarwar, A., andSharma, B. R. (2010).“Challenges and Prospects of Sustainable Groundwater Management in the Indus Basin, Pakistan.” Water Resources Management, Springer, 24(8), 1551–1569.
Scanlon, B. R., Fakhreddine, S., Rateb, A., deGraaf, I., Famiglietti, J., Gleeson, T., Grafton, R. Q., Jobbagy, E., Kebede, S., Kolusu, S. R., Konikow, L. F., Long, D., Mekonnen, M., Schmied, H. M., Mukherjee, A., MacDonald, A., Reedy, R. C., Shamsudduha, M., Simmons, C. T., Sun, A., Taylor, R. G., Villholth, K. G., Vörösmarty, C. J., andZheng, C. (2023).“Global water resources and the role of groundwater in a resilient water future.” Nature Reviews Earth and Environment, Springer Nature, 4(2), 87–101.
scipy.optimize.curve_fit. (n.d.).“scipy.optimize.curve_fit — SciPy v1.10.1 Manual.” <https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html> (Apr.27, 2023).
Shih, D. C. F., Lee, C. D., Chiou, K. F., andTsai, S. M. (2000).“Spectral analysis of tidal fluctuations in ground water level.” Journal of the American Water Resources Association, 36(5), 1087–1099.
Sun, J., Hu, L., Li, D., Sun, K., andYang, Z. (2022).“Data-driven models for accurate groundwater level prediction and their practical significance in groundwater management.” Journal of Hydrology, Elsevier, 608, 127630.
Suryoputro, N., Suhardjono, Soetopo, W., andSuhartanto, E. (2017).“Calibration of infiltration parameters on hydrological tank model using runoff coefficient of rational method.” AIP Conference Proceedings, 1887(September 2017).
Tapoglou, E., Karatzas, G. P., Trichakis, I. C., andVarouchakis, E. A. (2014).“A spatio-temporal hybrid neural network-Kriging model for groundwater level simulation.” Journal of Hydrology, Elsevier B.V., 519(PD), 3193–3203.
Vandenberghe, L. (2021).“9 . Least squares data fitting.” (Spring).
Wang, W., andLu, Y. (2018).“Analysis of the Mean Absolute Error (MAE) and the Root Mean Square Error (RMSE) in Assessing Rounding Model.” IOP Conference Series: Materials Science and Engineering, IOP Publishing, 324(1), 012049.
Wei, Z. lei, Wang, D. fei, Sun, H. yue, andYan, X. (2020).“Comparison of a physical model and phenomenological model to forecast groundwater levels in a rainfall-induced deep-seated landslide.” Journal of Hydrology, Elsevier, 586, 124894.
Yoon, H., Hyun, Y., Ha, K., Lee, K. K., andKim, G. B. (2016).“A method to improve the stability and accuracy of ANN- and SVM-based time series models for long-term groundwater level predictions.” Computers & Geosciences, Pergamon, 90, 144–155.
Yuan, S. (2022).“Review of Root-Mean-Square Error Calculation Methods for Large Deployable Mesh Reflectors.” International Journal of Aerospace Engineering, Hindawi Limited, 2022.