@article{PathirajaAnghileriBurlandoetal.2017, author = {Pathiraja, Sahani Darschika and Anghileri, Daniela and Burlando, P. and Sharma, A. and Marshall, L. and Moradkhani, H.}, title = {Insights on the impact of systematic model errors on data assimilation performance in changing catchments}, series = {Advances in water resources}, volume = {113}, journal = {Advances in water resources}, publisher = {Elsevier}, address = {Oxford}, issn = {0309-1708}, doi = {10.1016/j.advwatres.2017.12.006}, pages = {202 -- 222}, year = {2017}, abstract = {The global prevalence of rapid and extensive land use change necessitates hydrologic modelling methodologies capable of handling non-stationarity. This is particularly true in the context of Hydrologic Forecasting using Data Assimilation. Data Assimilation has been shown to dramatically improve forecast skill in hydrologic and meteorological applications, although such improvements are conditional on using bias-free observations and model simulations. A hydrologic model calibrated to a particular set of land cover conditions has the potential to produce biased simulations when the catchment is disturbed. This paper sheds new light on the impacts of bias or systematic errors in hydrologic data assimilation, in the context of forecasting in catchments with changing land surface conditions and a model calibrated to pre-change conditions. We posit that in such cases, the impact of systematic model errors on assimilation or forecast quality is dependent on the inherent prediction uncertainty that persists even in pre-change conditions. Through experiments on a range of catchments, we develop a conceptual relationship between total prediction uncertainty and the impacts of land cover changes on the hydrologic regime to demonstrate how forecast quality is affected when using state estimation Data Assimilation with no modifications to account for land cover changes. This work shows that systematic model errors as a result of changing or changed catchment conditions do not always necessitate adjustments to the modelling or assimilation methodology, for instance through re-calibration of the hydrologic model, time varying model parameters or revised offline/online bias estimation.}, language = {en} } @article{PathirajaMoradkhaniMarshalletal.2018, author = {Pathiraja, Sahani Darschika and Moradkhani, H. and Marshall, L. and Sharma, Ashish and Geenens, G.}, title = {Data-driven model uncertainty estimation in hydrologic data assimilation}, series = {Water resources research : WRR / American Geophysical Union}, volume = {54}, journal = {Water resources research : WRR / American Geophysical Union}, number = {2}, publisher = {American Geophysical Union}, address = {Washington}, issn = {0043-1397}, doi = {10.1002/2018WR022627}, pages = {1252 -- 1280}, year = {2018}, abstract = {The increasing availability of earth observations necessitates mathematical methods to optimally combine such data with hydrologic models. Several algorithms exist for such purposes, under the umbrella of data assimilation (DA). However, DA methods are often applied in a suboptimal fashion for complex real-world problems, due largely to several practical implementation issues. One such issue is error characterization, which is known to be critical for a successful assimilation. Mischaracterized errors lead to suboptimal forecasts, and in the worst case, to degraded estimates even compared to the no assimilation case. Model uncertainty characterization has received little attention relative to other aspects of DA science. Traditional methods rely on subjective, ad hoc tuning factors or parametric distribution assumptions that may not always be applicable. We propose a novel data-driven approach (named SDMU) to model uncertainty characterization for DA studies where (1) the system states are partially observed and (2) minimal prior knowledge of the model error processes is available, except that the errors display state dependence. It includes an approach for estimating the uncertainty in hidden model states, with the end goal of improving predictions of observed variables. The SDMU is therefore suited to DA studies where the observed variables are of primary interest. Its efficacy is demonstrated through a synthetic case study with low-dimensional chaotic dynamics and a real hydrologic experiment for one-day-ahead streamflow forecasting. In both experiments, the proposed method leads to substantial improvements in the hidden states and observed system outputs over a standard method involving perturbation with Gaussian noise.}, language = {en} } @article{PathirajaAnghileriBurlandoetal.2018, author = {Pathiraja, Sahani Darschika and Anghileri, Daniela and Burlando, Paolo and Sharma, Ashish and Marshall, Lucy and Moradkhani, Hamid}, title = {Time-varying parameter models for catchments with land use change}, series = {Hydrology and earth system sciences : HESS}, volume = {22}, journal = {Hydrology and earth system sciences : HESS}, number = {5}, publisher = {Copernicus}, address = {G{\"o}ttingen}, issn = {1027-5606}, doi = {10.5194/hess-22-2903-2018}, pages = {2903 -- 2919}, year = {2018}, abstract = {Rapid population and economic growth in Southeast Asia has been accompanied by extensive land use change with consequent impacts on catchment hydrology. Modeling methodologies capable of handling changing land use conditions are therefore becoming ever more important and are receiving increasing attention from hydrologists. A recently developed data-assimilation-based framework that allows model parameters to vary through time in response to signals of change in observations is considered for a medium-sized catchment (2880 km(2)) in northern Vietnam experiencing substantial but gradual land cover change. We investigate the efficacy of the method as well as the importance of the chosen model structure in ensuring the success of a time-varying parameter method. The method was used with two lumped daily conceptual models (HBV and HyMOD) that gave good-quality streamflow predictions during pre-change conditions. Although both time-varying parameter models gave improved streamflow predictions under changed conditions compared to the time-invariant parameter model, persistent biases for low flows were apparent in the HyMOD case. It was found that HyMOD was not suited to representing the modified baseflow conditions, resulting in extreme and unrealistic time-varying parameter estimates. This work shows that the chosen model can be critical for ensuring the time-varying parameter framework successfully models streamflow under changing land cover conditions. It can also be used to determine whether land cover changes (and not just meteorological factors) contribute to the observed hydrologic changes in retrospective studies where the lack of a paired control catchment precludes such an assessment.}, language = {en} } @article{deWiljesPathirajaReich2020, author = {de Wiljes, Jana and Pathiraja, Sahani Darschika and Reich, Sebastian}, title = {Ensemble transform algorithms for nonlinear smoothing problems}, series = {SIAM journal on scientific computing}, volume = {42}, journal = {SIAM journal on scientific computing}, number = {1}, publisher = {Society for Industrial and Applied Mathematics}, address = {Philadelphia}, issn = {1064-8275}, doi = {10.1137/19M1239544}, pages = {A87 -- A114}, year = {2020}, abstract = {Several numerical tools designed to overcome the challenges of smoothing in a non-linear and non-Gaussian setting are investigated for a class of particle smoothers. The considered family of smoothers is induced by the class of linear ensemble transform filters which contains classical filters such as the stochastic ensemble Kalman filter, the ensemble square root filter, and the recently introduced nonlinear ensemble transform filter. Further the ensemble transform particle smoother is introduced and particularly highlighted as it is consistent in the particle limit and does not require assumptions with respect to the family of the posterior distribution. The linear update pattern of the considered class of linear ensemble transform smoothers allows one to implement important supplementary techniques such as adaptive spread corrections, hybrid formulations, and localization in order to facilitate their application to complex estimation problems. These additional features are derived and numerically investigated for a sequence of increasingly challenging test problems.}, language = {en} } @article{GaidzikPathirajaSaalfeldetal.2020, author = {Gaidzik, Franziska and Pathiraja, Sahani Darschika and Saalfeld, Sylvia and Stucht, Daniel and Speck, Oliver and Thevenin, Dominique and Janiga, Gabor}, title = {Hemodynamic data assimilation in a subject-specific circle of Willis geometry}, series = {Clinical Neuroradiology}, volume = {31}, journal = {Clinical Neuroradiology}, number = {3}, publisher = {Springer}, address = {Heidelberg}, issn = {1869-1439}, doi = {10.1007/s00062-020-00959-2}, pages = {643 -- 651}, year = {2020}, abstract = {Purpose The anatomy of the circle of Willis (CoW), the brain's main arterial blood supply system, strongly differs between individuals, resulting in highly variable flow fields and intracranial vascularization patterns. To predict subject-specific hemodynamics with high certainty, we propose a data assimilation (DA) approach that merges fully 4D phase-contrast magnetic resonance imaging (PC-MRI) data with a numerical model in the form of computational fluid dynamics (CFD) simulations. Methods To the best of our knowledge, this study is the first to provide a transient state estimate for the three-dimensional velocity field in a subject-specific CoW geometry using DA. High-resolution velocity state estimates are obtained using the local ensemble transform Kalman filter (LETKF). Results Quantitative evaluation shows a considerable reduction (up to 90\%) in the uncertainty of the velocity field state estimate after the data assimilation step. Velocity values in vessel areas that are below the resolution of the PC-MRI data (e.g., in posterior communicating arteries) are provided. Furthermore, the uncertainty of the analysis-based wall shear stress distribution is reduced by a factor of 2 for the data assimilation approach when compared to the CFD model alone. Conclusion This study demonstrates the potential of data assimilation to provide detailed information on vascular flow, and to reduce the uncertainty in such estimates by combining various sources of data in a statistically appropriate fashion.}, language = {en} } @article{PathirajaReichStannat2021, author = {Pathiraja, Sahani Darschika and Reich, Sebastian and Stannat, Wilhelm}, title = {McKean-Vlasov SDEs in nonlinear filtering}, series = {SIAM journal on control and optimization : a publication of the Society for Industrial and Applied Mathematics}, volume = {59}, journal = {SIAM journal on control and optimization : a publication of the Society for Industrial and Applied Mathematics}, number = {6}, publisher = {Society for Industrial and Applied Mathematics}, address = {Philadelphia}, issn = {0363-0129}, doi = {10.1137/20M1355197}, pages = {4188 -- 4215}, year = {2021}, abstract = {Various particle filters have been proposed over the last couple of decades with the common feature that the update step is governed by a type of control law. This feature makes them an attractive alternative to traditional sequential Monte Carlo which scales poorly with the state dimension due to weight degeneracy. This article proposes a unifying framework that allows us to systematically derive the McKean-Vlasov representations of these filters for the discrete time and continuous time observation case, taking inspiration from the smooth approximation of the data considered in [D. Crisan and J. Xiong, Stochastics, 82 (2010), pp. 53-68; J. M. Clark and D. Crisan, Probab. Theory Related Fields, 133 (2005), pp. 43-56]. We consider three filters that have been proposed in the literature and use this framework to derive Ito representations of their limiting forms as the approximation parameter delta -> 0. All filters require the solution of a Poisson equation defined on R-d, for which existence and uniqueness of solutions can be a nontrivial issue. We additionally establish conditions on the signal-observation system that ensures well-posedness of the weighted Poisson equation arising in one of the filters.}, language = {en} }