Assessment of Data Assimilation on Hydraulic Simulations of the River Demer
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Faculty of Bioscience Engineering Academic year 2014-2015 Assessment of data assimilation on hydraulic simulations of the river Demer Joline De Smedt Promotor: Prof. Dr. ir. Niko Verhoest Tutor: ir. Katrien Van Eerdenbrugh, ir. Niels De Vleeschouwer Master's dissertation submitted in fulfillment of the requirements for the degree of Master of Science in Bioscience Engineering: Land and Water Management Faculty of Bioscience Engineering Academic year 2014-2015 Assessment of data assimilation on hydraulic simulations of the river Demer Joline De Smedt Promotor: Prof. Dr. ir. Niko Verhoest Tutor: ir. Katrien Van Eerdenbrugh, ir. Niels De Vleeschouwer Master's dissertation submitted in fulfillment of the requirements for the degree of Master of Science in Bioscience Engineering: Land and Water Management De auteur en promotor geven de toelating deze scriptie voor consultatie beschikbaar te stellen en delen ervan te kopi¨erenvoor persoonlijk gebruik. Elk ander gebruik valt onder de beperkingen van het auteursrecht, in het bijzonder met betrekking tot de verplichting uitdrukkelijk de bron te vermelden bij het aanhalen van resultaten uit deze scriptie. The author and promoter give the permission to use this thesis for consultation and to copy parts of it for personal use. Every other use is subject to the copyright laws, more specifically the source must be extensively specified when using results from this thesis. Ghent, June 2015 De promotor, De tutoren, Prof. dr. ir. Niko Verhoest ir. Katrien Van Eerdenbrugh, ir. Niels De Vleeschouwer De auteur, Joline De Smedt Preface In front of you lies the final piece of the puzzle on how to become a bio-engineer. As with all puzzles, this one also consists of many pieces. Hard work, focus and the necessary complications were a few of those pieces but the majority consisted of making new friends, getting to know my own strengths and weaknesses, enjoying life and gaining more and more interest in the subject of land and water management. The latter would not have been possible without the interesting courses, given by professors and assistants passionate about their field of study. Their devotion and enthusiasm convinced me to attend almost every class, over and over again in the last five years. I would especially like to thank professor Niko Verhoest. Not only did he increase my interest in water related topics, he also provided me with help and guidance on my thesis in this last year. I would also like to thank my tutors Katrien Van Eerdenbrugh and Niels De Vleeschouwer. The patience with which they answered all of my questions and the time they took to help and guide me in the right direction are strongly appreciated. Also the company DHI and in particular Henrik Madsen should not be forgotten. The stay they offered me in their main office in Denmark gave me the opportunity to learn more about the MIKE 11 model as well as provided me with the chance of visiting the beautiful country of Denmark. A special thanks goes to my parents. I understand that it is not self-evident to trust and support a daughter during six years of study, five years of living on her own in Ghent and half a year of living in Sweden on Erasmus. They did this however without ever doubting me or my capacity of completing this adventure. I would also like to thank them and my sister for their patience with me during the completion of my thesis although they did not completely understand what I was doing. Next, I would like to thank Alexandra Van Wesemael. Thank you for sharing the good as well ad the bad moments in our thesis time together, for sheering me up with songs, cookies and advice and for not losing hope in these last months. Finally, I would like to thank all of my friends for supporting me and forcing me to look on the bright side of life, in particular Lotte Moens. Thank you Lotte, for bringing me cake and listening to my endless complaining when I needed it. Also a thank you to Jonas Uyttersprot, who was always there for me even though he had his own thesis to write. I couldn't have completed this task without the support and guidance of all of them. Joline De Smedt, June 2015 i ii Abstract To be able to prepare for the future and protect ourselves from possible disasters, forecasts of future rainfall, temperature, discharge in a river system and many more environmental variables are issued. Data assimilation is in these cases applied to improve the predictions, resulting in a better preparation and protection against upcoming problems. It can thus be said that the impact of data assimilation is significant. In this study, a comparison is made between the two data assimilation algorithms implemented in the DA software of MIKE 11 created by DHI. Moreover both the application of observations of discharge as the application of observations of water level are tested. An analysis is made of the Kalman gain obtained from the EnKF simulation run, while for the WF the amplitude A and the interval of influence are examined. Finally the improvements in the model prediction are validated using a synthetic experiment. The results of this study indicate that, though the time required to complete a model run is considerably larger compared to the WF, a slightly more accurate prediction of the true state is obtained using the EnKF DA algorithm. A substantial improvement is already achieved with the application of the WF DA algorithm despite the poor approximation of the true shape of the Kalman gain by the implemented gain functions. In addition, no significant effect of the shape of the gain function was found. It is however not possible to procure an estimation of the uncertainty of the model run with a WF simulation. Finally, the implementation of DA procedures on the model of the Demer river revealed issues regarding the stability of the DA software. Especially with the application of the EnKF procedure with observations of water level, severe instabilities were encountered using the model of the Demer river. iii iv Samenvatting Om de mensheid en zijn omgeving te beschermen tegen mogelijke rampen, worden op regel- matige basis voorspellingen uitgevoerd van verschillende variabelen zoals neerslag, temperatuur, debiet in een rivier en dergelijke meer. Hierbij wordt vaak data assimilatie toegepast om betere voorspellingen te bekomen. Dit leidt tot de mogelijkheid om een betere voorbereiding te treffen en dus op die manier een betere bescherming te garanderen tegen wat in de toekomst zou kunnen voorkomen. In dit onderzoek worden twee data assimilatie procedures bekeken die reeds zijn ge¨ımplementeerd in de MIKE 11 software ontwikkeld door DHI. Daarnaast wordt ook het gebruik van zowel tijdsreeksen van debiet als het gebruik van tijdsreeksen van waterhoogte ge¨evalueerd. Een analyse van de Kalman gain verkregen uit de Ensemble Kalman filter (EnKF) simulaties wordt uitgevoerd. Ook wordt er onderzoek gevoerd naar de amplitude voor de weighting func- tion (WF) simulatie en het interval waarover een invloed merkbaar is. Als laatste worden de verbeteringen in de modelvoorspelling gevalideerd met behulp van een synthetisch experiment. Uit deze studie blijkt dat een iets meer accurate voorspelling wordt bekomen wanneer gebruikt wordt gemaakt van de EnKF procedure dan wanneer de WF procedure wordt aangewend. Hi- ertegenover staat dan wel dat de simulatie met de EnKF procedure beduidend langer duurt. Ook de voorspelling met de WF toont een duidelijke verbetering tegenover de voorspelling zon- der aanwending van data assimilatie, al moet hierbij worden opgemerkt dat de verschillende mogelijke vormen van de gain functies uit de WF geen goede representatie zijn voor het verloop van de Kalman gain. Echter, aangezien wordt aangetoond dat de vorm van de gain functie in dit geval weinig tot geen invloed heeft op de grootte van de aanpassing, vormt dit geen probleem. Daarnaast is het ook zo dat met deze DA procedure het niet mogelijk is om een inschatting te verkrijgen van de onzekerheid op de modelvoorspelling. Een laatste bevinding uit dit onderzoek is dat bij gebruik van de DA procedures mogelijks problemen met de stabiliteit ondervonden worden. Voornamelijk bij de implementatie van de EnKF procedure met gebruik van waterhoogte in het model van de Demer komen ernstige instabiliteiten voor. v vi Contents Preface i Abstract iii Samenvatting v List of Figures ix List of Tables xiii List of Abbreviations xv 1 Introduction 1 2 Brief introduction to data assimilation 3 2.1 The weighting function . 4 2.2 The Kalman filter . 6 2.2.1 Discrete Kalman filter . 7 2.2.2 Extended Kalman Filter . 8 2.2.3 Ensemble Kalman Filter . 10 3 Location 13 3.1 The Demer and its catchment . 13 3.2 Water management . 15 3.3 Calibration and validation data . 15 4 The model 17 4.1 Reduced model . 18 4.2 Boundaries . 20 4.3 Initial conditions . 21 4.4 Uncertainty . 21 4.5 Model forecast . 23 vii Contents viii 5 Methodology 25 5.1 Step 1 and 2: Ensemble Kalman filter . 25 5.2 Step 3 to 6: Weighting function . 26 5.3 Step 7: Validation . 27 6 Results and discussion 29 6.1 EnKF with observations of discharge . 29 6.2 EnKF with observations of water level . 30 6.3 Analysis of Kalman gain K .............................. 30 6.3.1 General observations . 32 6.3.2 Evolution of K ................................. 36 6.4 Amplitude A ...................................... 44 6.5 Interval of influence . 45 6.6 WF with observations of discharge . 48 6.7 WF with observations of water level . 57 6.8 Validation . 60 6.8.1 WF vs EnKF performance . 65 6.8.2 Limitations . 68 7 Conclusion 69 7.1 Suggestions for future research .