RESIDUE-CORRECTION-BASED DATA ASSIMILATION IN COASTAL HYDRODYNAMICS (WITH AN APPLICATION TO SINGAPORE REGIONAL MODEL) WANG XUAN (M.Sc., TJU) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2012     Acknowledgements I wish to express my deepest and heartfelt gratitude to my supervisor, Assoc. Professor Vladan Babovic, who guided me throughout this research, and gave me the opportunity to work with other researchers in Singapore-Delft Water Alliance. It is with his invaluable advice, continuous support, and crucial encouragement that I can tackle various challenges and achieve my research goals. I would like to convey my sincere gratitude to Dr. Herman Gerritsen (Delatares) and Dr. Henk van den Boogaard (Delatares), for their insightful comments and encouragement on this research. Special thanks to Dr. Raghu Rao, Dr. Abhijit Badwe and Dr. Rama Rao, who proposed numerous inspiring ideas on my research. The stimulating discussions with them have established a solid basis for this thesis. Thanks are extended to my colleagues in Singapore-Delft Water Alliance, Dr. Galelli Stefano, Dr. Zhang Jingjie, Dr. Ooi SK, Dr.Sun Yabin, Ms. Tay Hui Xin Serene, Mr. Alamsyah Kurniawan, Ms. Arunoda as well as my colleagues in Deltares, Dr. Ann Piyamarn Sisomphon, Dr. Ghada Elserafy, Dr. Julius Sumihar, Prof. Martin Verlaan, for the enjoyable working experience we share together. The support and contributions from the Singapore-Delft Water Alliance (SDWA) and the National University of Singapore are gratefully acknowledged, for granting me the research scholarship and providing me with a stimulating research environment from which I benefited greatly. I also thank Maritime Port Authority (MPA), i    Singapore and University of Hawaii Sea Level Center (UHSLC) for providing the local maritime data for analysis. Additional thanks to my friends, Dr.Yi Jiangtao, Mr. Wang Shanquan, Ms. Zhang Nan and Mr. Wang Li, for all the great time we spent together. Last but not the least, I would like to express my heartfelt thankfulness to my beloved parents who continuously support me with their love. Without their supporting and understanding, I would not reach so far. ii    Table of Contents Acknowledgements i  Table of Contents . iii  Summary . vi  List of Tables ix  List of Figures . xi  List of Symbols xv  Chapter Introduction . 1  1.1 Research background 1  1.2 Objective . 3  1.3 Organization 7  Chapter Literature review 9  2.1 Hydrodynamic modeling . 9  2.2 Review of data assimilation 10  2.2.1 Development of data assimilation 10  2.2.2 Classification or Data assimilation strategies 12  2.3 Development of time series forecast . 14  2.4 Development of spatial distribution 16  2.5 Summary and conclusion 19  Chapter Numerical model and study area . 22  3.1 Delft-3D Flow . 22  iii   3.1.1 Introduction 22  3.1.2 Conceptual Description 22  3.2 Singapore Regional Model 24  3.2.1 Model Set-up 25  3.2.2 Model Simulation . 27  3.2.3 Discussion 28  Chapter Methodologies 36  4.1 Methods for time series forecast of model residue 36  4.1.1 Time lagged recurrent network (TLRN) 36  4.1.2 Modified local model (MLM) 38  4.2 Methods for spatial distribution of model residue . 48  4.2.1 Approximated Ordinary Kriging(AOK) . 48  4.2.2 Approximated time-space Ordinary Kriging (ASTOK) . 56  4.2.3 Unscented Kalman filter (UKF) . 58  4.2.4 Two-sample Kalman filter (two-sample KF) . 62  Chapter Application of model residue forecast to SRM(C) . 72  5.1 Introduction . 72  5.2 Application of TLRN in the residue forecast 74  5.2.1 Construction of TLRN for SRM(C) correction 74  5.2.2 Results 76  5.3 Application of modified local model in the residue forecast 78  5.3.1 Construction of LM and MLM for SRM(C) correction . 78  iv    5.3.2 Results 81  5.4 Comparison between TLRN and MLM 84  Chapter Application of spatial correction to SRM(C) . 103  6.1 Introduction . 103  6.2 Application of Kriging in the spatial distribution . 104  6.2.1 Construction of AOK for SRM(C) correction . 104  6.2.2 Results of AOK 105  6.2.3 Construction of ASTOK for SRM(C) correction . 108  6.2.4 Results of ASTOK . 110  6.2.5 Comparison 112  6.3 Application of Kalman filter in the spatial distribution 115  6.3.1 Construction of UKF for SRM(C) correction 115  6.3.2 Results of UKF 116  6.3.3 Construction of two-sample KF for SRM(C) correction . 118  6.3.4 Results of two-sample KF 119  6.3.5 Comparison between UKF and two-sample KF 119  6.4 Comparison between Kriging and Kalman filter 121  Chapter Application of Data assimilation to SRM(F) 156  Chapter Conclusions and Recommendations 161  8.1 Conclusions . 161  8.2 Recommendations . 164  Reference 167  v   Summary Singapore Regional Model was developed to predict the water motion in Singapore Straits. It, however, like other numerical models, suffers from limitations arising from parameter uncertainty, simplified assumptions, absence of data for appropriate specification of boundary conditions and etc. Moreover, since the water motion in Singapore Straits is driven by tides from both South China Sea and Andaman Sea, complex hydrodynamics adds to the difficulties of accurate simulations. In view of the above, the data assimilation was investigated in this study to enhance the performance of Singapore Regional Model. Based on the concept of model residue prediction, distribution and following correction, several techniques have successfully been developed and implemented to improve the forecasting accuracy of water level around Singapore area. As for the model residue predictions, unlike most previous research which tended to take only account of historical records, a special attention has been given to a prior estimate apart from the historical records in this study. The influence of a prior estimate was thoroughly examined through the method of time lagged recurrent network (TLRN). The results suggest that additional consideration of a prior estimate is instrumental to improve the data-driven procedure like TLRN. Besides, a modified local model (MLM) has been developed based on chaos theory, which took a prior estimate into construction of phase space. It can not only retain the advantage of conventional LM, but also yield more stable results over the long vi    horizons. Since MLM searches for the optimal embedding parameters only at the beginning of entire calculation, it has better computational efficiency. The predicted model residues at measured station were then distributed spatially to non-measured stations, which were used to correct the model output at these stations. As the spatial distribution becomes extremely difficult in situations with few sample stations at a highly non-linear system, the Approximated Ordinary Kriging (AOK) which is particularly suited to scenarios with only sparse sample data was resorted to. Both the space and time lags were then taken into consideration in the AOK implementation (also known as “ASTOK”). The results indicate that consideration of the time lag between different locations was conducive to capture the spatial relationship. Incorporating the updated data with appropriate time lag from measured locations can enhance the interpolation ability. In addition to Kriging, Kalman filter (KF) was another data assimilation technique which the present research has explored. As the conventional KF approach suffers from limitation due to the updated initial conditions which was quickly ‘wash-out’ after a certain forecast horizon, this study explored two different Kalman Filter approaches, namely two-sample Kalman filter (two-sample KF) and Unscented Kalman filter (UKF) to avoid the preceding limitation. In conclusion, the combined use of MLM and ASTOK was found to be fairly effective in improving the predictive efficacy of Singapore Regional model (SRM), with high efficiency in computation. It can effectively correct outputs of SRM even with coarse resolution and improve the accuracy over the entire domain (especially vii   for long forecast horizons). These corrected results of numerical model can thus sever better to provide information of Singapore regional water. viii    Chapter Application of Data assimilation to SRM(F) Figure 7.3 Comparison between RMSE of corrected SRM(C) and corrected SRM(F) at Tanah Merah (using AOK) Figure 7.4 Comparison between RMSE of corrected SRM(C) and corrected SRM(F) at Sembawang (using AOK) 159   Chapter Application of Data assimilation to SRM(F) Figure 7.5 Comparison between RMSE of corrected SRM(C) and corrected SRM(F) at Raffles (using AOK) 160    Chapter Conclusions and Recommendations Chapter Conclusions and Recommendations 8.1 Conclusions This study explores residue-correction based data assimilation scheme which is conceived to correct the numerical outputs of coarse version of Singapore Regional Model (SRM(C)) so as to improve its forecast accuracy. The proposed scheme comprises of two phases, namely residue prediction and spatial distribution. In the first phase (i.e. residue prediction), model residue prediction is first carried out at measured stations using time lagged recurrent network (TLRN) with different inputs. The prediction results suggest that TLRN with two predictors (namely historical residue  mea (t n ) and a prior estimate at the forecast time level x mea (t n  t ) ) is superior to TLRN with one predictor (namely historical residue  mea (t n ) ) for all forecast horizons at every station. The inclusion of a prior estimate at the forecast time level x mea (t n  t ) in the TLRN turns out to be very helpful to improve its prediction accuracy. It also implies that the additional consideration of physical information such as a prior estimate is instrumental to enhance the performance of data-driven procedure like TLRN. Apart from the TLRN method, the conventional local model (LM) based on chaos theorem is also tested in this study for model residue prediction. Although LM approach is found to be effective for model residue prediction over the short horizons, its performance for the long horizons is less satisfactory. A modified local model (MLM) is thereby developed in this research which can fairly produce desirable predictions over not only the short but also long horizons. It retains the advantage of conventional LM to uncover the trajectories of model residue through 161   Chapter Conclusions and Recommendations embedding phase space and yet yield more stable results over the long horizons. This is achieved by taking a prior estimate into the local model calculation. What’s more, MLM searches for the optimal embedding parameters only at the beginning of the entire calculation, rather than at every prediction horizon as the way LM does. As such, it is more efficient in computation. In the second phase, spatial distribution is conducted at non-measured stations to estimate their model residues. Those predicted model residues from the first phase (more precisely from TLRN and MLM methods) are distributed from the two measured stations to the three non-measured ones. Unlike the previous work (Sun, 2010) where the distribution efficacy was guaranteed by selecting measured stations appropriately, this study attains desirable distribution performance with given measured stations by improving distribution approaches including Kriging and Kalman filter. The Approximated Ordinary Kriging (AOK) is first utilized which considers only the spatial correlation between measured and non-measured stations. Subsequently, the temporal correlation is further taken into account in the so-called Approximated Space-Time Ordinary Kriging (ASTOK). Although both AOK and ASTOK are found to be competent to capture complex, dynamic and non-linear spatial relationship, more favorable distribution performance is achieved by ASTOK in particular in short horizons. Several important messages are therefore attainable from the results of Kriging. The spatial relationship of model residues can sensibly be estimated through approximated variogram. It is feasible to calculate such variogram from the prior estimate offered by the SRM(C). The inclusion of time lag between 162    Chapter Conclusions and Recommendations different locations can contribute to improving the estimation of spatial relationship. Considering updated data with appropriate time lag from measured locations can enhance the distribution efficacy of Kriging. In addition to the Kriging method, two-sample Kalman filter and Unscented Kalman filter (UKF) are also examined in this study. While both approaches yield acceptable distribution results, UKF gives relatively better performance especially at those stations near coastal area. It may be attributed to the inclusion of two extra observation variables that are the model residues at two measured stations. Another contribution factor comes from the use of non-linear transformation function in the UKF approach. It employs Genetic Programming considering the underlying relationship between the model residue and the model output. It is noted that the model residues at measured locations can provide valuable information for the construction of the spatial correlation matrix. In general, the performance of AOK outdoes two-sample KF, and the UKF can compete with the preceding AOK, yet not on a par with ASTOK. It implies that the correction procedure to update the model reside (ASTOK and AOK) is more effective than the procedure to update the model output (UKF and two-sample KF). No matter whether Kriging or KF is adopted, relatively accurate predictions of residues at measured stations are found to be pivotal for the success of distribution. Hence, improving the prediction accuracy is critical to enhance the distribution efficiency. Based on the prediction and distribution performance of the preceding different approaches, it is reasonable to propose a hybrid data assimilation scheme which makes use of MLM and ASTOK for the model residue prediction and distribution, 163   Chapter Conclusions and Recommendations respectively. The use of MLM can help to preclude the adverse influence of long forecast horizon for time series forecast. The adoption of ASTOK can produce satisfactory results even in the case with sparse sampling stations in that it takes both distance lag and time lag into consideration. In conclusion, the combination of MLM and ASTOK is recommended for long time forecasting, which is even applicable for the case with only sparse sample stations. The numerical model (SRM(C)) is proved to be used successfully as the background information for the data assimilation scheme. Since the proposed scheme is designed to correct outputs of numerical model (SRM(C)), it can thus be executed offline without the need to interrupt SRM(C) calculation. After its implementation, results from SRM(C) become much more accurate, even better than those from original SRM(F). It confirms the advantages of the proposed scheme in terms of efficacy and efficiency. The corrected results of numerical model (SRM(C)) can provide useful information for the study of Singapore regional water. The proposed data assimilation scheme may have wider applications for engineer to improve model outputs of highly non-linear systems. 8.2 Recommendations One important assumption adopted in the present study is that the residue is distributed the same way that numerical model output is. The spatial dependence structure is estimated based on a prior estimate from numerical model output. As a result, the numerical simulation accuracy unavoidably affects the data assimilation efficacy. Further study is recommended to avoid such assumption. Besides, more 164    Chapter Conclusions and Recommendations works should be done in exploring other methods (besides Genetic Programming) and investigation more stations surrounding the Singapore Island. (a) Estimate the spatial relationship or spatial dependence structure based on model residue. This study estimates the spatial dependence structure based on a prior estimate. Since the variable to be interpolated is the model residue, although the numerical model output can be used to approximate the spatial relationship, it should be more sensible to estimate the spatial dependence structure based on the actual model residue. (b) In the case with a sufficient amount of measured stations, the data-rich information should be taken full advantage of to estimate the spatial relationship more reasonably. If that is the case, the spatial interpolation methods (like Kriging) with artificial neural network are recommended. (c) Evaluate some other intelligent methods other than Genetic Programming in estimating the observation transform functions. The present study makes use of Genetic Programming to estimate observation transform function of UKF. In future, more attempts are suggested to try some other intelligent methods, such as support vector machine, radial basis function network, etc. (d) Lay more stress on wider area surrounding Singapore Island. This took only five stations around Singapore islands as example to examine the performance of proposed data assimilation scheme. Scope of further study should be broadened to include wider areas surrounding the Singapore Island such that more stations can be chosen for evaluation. 165   Chapter Conclusions and Recommendations (e) This study applied the proposed scheme in hydrodynamic model to improve the water level forecasting. 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Numerical study of the tide and tidal dynamics in the South China Sea. Deep-Sea Res Pt I, 55(2): 137-154. 174    [...]... with only a handful of sample points Such scheme can be applied to improve the forecasting accuracy of water level around Singapore area and also provide useful information for other study of Singapore regional water In more specific terms, research objectives include: (a) To assess the performance of TLRN based on different predictors in the model residue prediction and to analyze the influence of... by Mancarella et al (2008) , the systematic model residue can be predicted by the residue correction scheme In this research, a hybrid data assimilation method based on the residue correction is explored which aims to improve the water level outputs generated by Singapore Regional Model 1.2 Objective As stated above, this study adopts a data assimilation method based on the residue correction The model. .. numerical model output directly The model output can be updated either in terms of state variables or model residue, and the updated variables or residue can then be assimilated into the model to improve estimates of system state at future time levels (Babovic and Fuhrman, 2002) Relatively speaking, updating model output in terms of model residue is more preferable since it has more physical insights... al., 2008), the Singapore Strait area (Chen et al., 2005; Chan et al., 2006) and the Malacca Strait up to the Andaman Sea (AS) region (Hii et al., 2006; Ibrahim and Yanagi, 2006) But the lack of detailed bathymetry data hampered the tidal analysis for numerical model Several modeling studies addressed the tide in the Singapore Strait (Shankar et al., 1997; Zhang and Gin, 2000; Pang and Tkalich, 2003;... different predictors 6    Chapter 1 Introduction (b) To enhance the application of LM and explore the potential of MLM in offering maintained forecast accuracy at various horizons (c) To estimate the spatial correlation between different stations for the case with only sparse sample data and interpolate data based on Ordinary Kriging theory by exploring both spatial and time lags (d) To apply the KF to update... water motion in 2    Chapter 1 Introduction Singapore Straits However, like other numerical models, it also suffers from limitations introduced by parameter uncertainty, simplified assumptions, and absence of data for appropriate specification of boundary initial conditions Moreover, since the Singapore Island is located between South China Sea and Andaman Sea and the water motion in Singapore Straits... further improved In order to analyze the tidal sensitivity, Kurniawan et al (Kurniawan et al., 2011) suggested using OpenDA approach of combine the observational data with the numerical model The Data assimilation idea is employed in this study, while it is mainly applied for the sensitivity analysis To further minimize the systematic model errors, later application in combination with data assimilation. .. limited insight into physical mechanisms, simplified assumptions, absence of data for proper setting of boundary conditions and model parameterizations and so on (Babovic et al., 2001; Vojinovic and Kecman, 2003; van den Boogaard and Mynett, 2004; Sun, 2010) As a consequence, the simulation is inevitably accompanied by a considerable amount of model residues To overcome the weakness, the method of data assimilation. .. distribution The hydrodynamic modeling system Singapore Regional Model (Fine and Coarse version) within Delft3D-FLOW is introduced in Chapter 3 Chapter 4 elaborates on the methods utilized in this study, including the TLRN, MLM, AOK and ATOK, two-sample KF and UKF Chapter 5 applies the residue prediction at measured station of coarse SRM (SRM(C)) using TLRN and 7   Chapter 1 Introduction  MLM The conventional... to the following steps: (i) Predicting the numerical model residues on measured stations using TLRN and MLM (ii) Distributing the forecasted residues to other grid locations through Kriging (AOK and ASTOK) and Kalman filter (two-sample KF and UKF) The primary objective of this study is to develop and implement applicable data assimilation scheme which is able to provide desirable forecasting at long .   RESIDUE-CORRECTION-BASED DATA ASSIMILATION IN COASTAL HYDRODYNAMICS (WITH AN APPLICATION TO SINGAPORE REGIONAL MODEL) WANG XUAN (M.Sc., TJU) A THESIS. hydrodynamics adds to the difficulties of accurate simulations. In view of the above, the data assimilation was investigated in this study to enhance the performance of Singapore Regional Model. . Dr.Yi Jiangtao, Mr. Wang Shanquan, Ms. Zhang Nan and Mr. Wang Li, for all the great time we spent together. Last but not the least, I would like to express my heartfelt thankfulness to my beloved