Lagrangian Data Assimilation for Improving Model Estimates of Velocity Fields and Residual Currents in a Tidal Estuary

Numerical models are associated with uncertainties that can be reduced through data assimilation (DA). Lower costs have driven a recent tendency to use Lagrangian instruments such as drifters and floats to obtain information about water bodies. However, difficulties emerge in their assimilation, since Lagrangian data are set out in a moving frame of reference and are not compatible with the fixed grid locations used in models to predict flow variables. We applied a pseudo-Lagrangian approach using OpenDA, an open-source DA tool to assimilate Lagrangian drifter data into an estuarine hydrodynamic model. Despite inherent challenges with using drifter datasets, the work showed that low-cost, low-resolution drifters can provide a relatively higher improvement over the Eulerian dataset due to the larger area coverage of the drifter. We showed that the assimilation of Lagrangian data obtained from GPS-tracked drifters in a tidal channel for a few hours can significantly improve modelled velocity fields (up to 30% herein). A 40% improvement in residual current direction was obtained when assimilating both Lagrangian and Eulerian data. We conclude that the best results are achieved when both Lagrangian and Eulerian datasets are assimilated into the hydrodynamic model.

A network-based perspective on coherent structure detection from very-sparse Lagrangian data

Coherent structure detection (CSD) is a long-lasting issue in fluid mechanics research as the presence of spatio-temporal coherent motion enables simpler ways to characterize the flow dynamics. Such reducedorder representation, in fact, has significant implications for the understanding of the dynamics of flows, as well as their modeling and control (Hussain, 1986). While the Eulerian framework has been extensively adopted for CSD, Lagrangian coherent structures have recently received increasing attention, mainly driven by advancements in Lagrangian flow measurement techniques (Haller, 2015; Hadjighasem et al., 2017). Lagrangian particle tracking (LPT), in particular, is widely used nowadays due to its ability to quantity fluid-parcel trajectories in three-dimensional volumes (Schanz et al., 2016).

Improving Ocean Circulations Using Lagrangian Data Assimilation of Surface Drifters During Grand Lagrangian Deployments

<p>Accurate forecast of ocean circulation is important in many aspects. A lack of direct ocean velocity observations has been one of the overarching issues in nowadays operational ocean data assimilation (DA) system. Satellite-tracked surface drifters, providing measurement of near-surface ocean currents, have been of increasing importance in global ocean observation system. In this work, the impact of an augmented-state Lagrangian data assimilation (LaDA) method using Local Ensemble Transform Filter (LETKF) is investigated within a realistic ocean DA system. We use direct location data from 300 surface drifters released in the Gulf of Mexico (GoM) by the Consortium for Advanced Research on Transport of Hydrocarbon in the Environment (CARTHE) during the summer 2012 Grand Lagrangian Deployment (GLAD) experiment. These drifter observations are directly assimilated into a realistic eddy-resolving GoM configuration of the Modular Ocean Model version 6 (MOM6) of the Geophysical Fluid Dynamics Laboratory (GFDL). Ocean states (T/S/U/V) are updated at both the surface and at depth by utilizing dynamic forecast error covariance statistics. Four experiments are conducted: (1) a free run generated by MOM6; 2) a DA experiment assimilating temperature and salinity profile observations from World Ocean Database 2018 (WOD18); and 3) a DA experiment assimilating both drifter and the profile observations. The LaDA results are then compared with the traditional assimilation using the drifter-derived velocity field from the same GLAD database. In addition, we evaluate the impact of the LaDA algorithm on different eddy-permitting and eddy-resolving model resolutions to determine the most effective horizontal resolutions for assimilating drifter position data using LaDA.</p>

Uncovering Fine-Scale Wave-Driven Transport Features in a Fringing Coral Reef System via Lagrangian Coherent Structures

Understanding the transport and exchange of water masses both within a reef and between a reef and the surrounding ocean is needed to describe a wide-range of ecosystem processes that are shaped by the movement of material and heat. We show how novel Lagrangian data processing methods, specifically developed to reveal key and often hidden transport structures, can help visualize flow transport patterns within and around morphologically complex reef systems. As an example case study, we consider the wave-driven flow transport within the Ningaloo Reef in Western Australia. We show that a network of attracting, repelling, and trapping flow transport structures organizes the flow transport into, around, and out of the reef. This approach is broadly applicable to coral reef systems, since the combination of well-defined bathymetry and persistent flow-forcing mechanisms (e.g., by wave breaking or tides) is conducive to the existence of persistent Lagrangian transport structures that organize material transport.

Lagrangian Reduced Order Modeling Using Finite Time Lyapunov Exponents

There are two main strategies for improving the projection-based reduced order model (ROM) accuracy—(i) improving the ROM, that is, adding new terms to the standard ROM; and (ii) improving the ROM basis, that is, constructing ROM bases that yield more accurate ROMs. In this paper, we use the latter. We propose two new Lagrangian inner products that we use together with Eulerian and Lagrangian data to construct two new Lagrangian ROMs, which we denote α-ROM and λ-ROM. We show that both Lagrangian ROMs are more accurate than the standard Eulerian ROMs, that is, ROMs that use standard Eulerian inner product and data to construct the ROM basis. Specifically, for the quasi-geostrophic equations, we show that the new Lagrangian ROMs are more accurate than the standard Eulerian ROMs in approximating not only Lagrangian fields (e.g., the finite time Lyapunov exponent (FTLE)), but also Eulerian fields (e.g., the streamfunction). In particular, the α-ROM can be orders of magnitude more accurate than the standard Eulerian ROMs. We emphasize that the new Lagrangian ROMs do not employ any closure modeling to model the effect of discarded modes (which is standard procedure for low-dimensional ROMs of complex nonlinear systems). Thus, the dramatic increase in the new Lagrangian ROMs’ accuracy is entirely due to the novel Lagrangian inner products used to build the Lagrangian ROM basis.

Lagrangian Data Assimilation of Surface Drifters to Support Ocean and Coupled Model Initialization

<p>The air-sea interface is one of the most physically active interfaces of the Earth's environments and significantly impacts the dynamics in both the atmosphere and ocean. In this study, we discuss the data assimilation of surface drifters, of which the dynamic motions are highly relevant to the instant change of both surface wind field and underlying ocean flow fields. We intend to take advantage of this relationship and improve the estimation of the model initialization in both ocean and coupled atmosphere-ocean systems.</p><p>The assimilation of position data from Lagrangian observing platforms is underdeveloped in operational applications because of two main challenges: 1) nonlinear growth of model and observation error in the Lagrangian trajectories, and 2) the high dimensionality of realistic models. In this study, we first propose an augemented-state Lagrangian data assimilation (LaDA) method that is based on the Local Ensemble Transform Kalman Filter (LETKF). The algorithm is tested with “identical twin” approach of Observing System Simulation Experiments (OSSEs) using the ocean model. Examinations on both of the eddy-permitting and the eddy-resolving Modular Ocean Model of the Geophysical Fluid Dynamics Laboratory (GFDL) are tested, which is intended to update the ocean states (T/S/U/V) at both the surface and at depth by directly assimilating the drifter locations. Results show that with a proper choice of localization radius, the LaDA can outperform conventional assimilation of surface in situ temperature and salinity measurements. The improvements are seen not only in the surface state estimate, but also throughout the ocean column to deep layer. The impacts of localization radius and model error in estimating accuracy of both fluid and drifter states are further investigated. In the second section, we investigate the LaDA within a Strongly Coupled Data Assimilation (SCDA) system using the simplified Modular Arbitrary-Order Ocean-Atmosphere Model (MAOOAM), a three-layer truncated quasi-geostrophic model. Results show that assimilating the surface drifter locations directly is capable of improving not only the ocean states but also the atmosphere states as well. We then compare it to the conventional approach to assimilate the approximated velocities instead of the direct drifter locations and it shows that the assimilating drifter locations outperforms the other approach.</p>

Improving the Accuracy of Hydrodynamic Model Predictions Using Lagrangian Calibration

While significant studies have been conducted in Intermittently Closed and Open Lakes and Lagoons (ICOLLs), very few have employed Lagrangian drifters. With recent attention on the use of GPS-tracked Lagrangian drifters to study the hydrodynamics of estuaries, there is a need to assess the potential for calibrating models using Lagrangian drifter data. Here, we calibrated and validated a hydrodynamic model in Currimundi Lake, Australia using both Eulerian and Lagrangian velocity field measurements in an open entrance condition. The results showed that there was a higher level of correlation (R2 = 0.94) between model output and observed velocity data for the Eulerian calibration compared to that of Lagrangian calibration (R2 = 0.56). This lack of correlation between model and Lagrangian data is a result of apparent difficulties in the use of Lagrangian data in Eulerian (fixed-mesh) hydrodynamic models. Furthermore, Eulerian and Lagrangian devices systematically observe different spatio-temporal scales in the flow with larger variability in the Lagrangian data. Despite these, the results show that Lagrangian calibration resulted in optimum Manning coefficients (n = 0.023) equivalent to those observed through Eulerian calibration. Therefore, Lagrangian data has the potential to be used in hydrodynamic model calibration in such aquatic systems.