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Optimizing a Drifter Cast Strategy with a Genetic Algorithm
Abstract
An experiment design problem–-that of drifter cast strategy–-is discussed. Different optimization techniques used as part of preparations for the Semaphore-93 air-sea experiment, during which drifters were deployed, are examined. The oceanographic experiment objective was to sample a 500-km-square zone cantered at 33°N, 22°W in the Azores current area, using an average of 25 surface drifters for at least one month. We investigate different “orders of merit” for determining the performance of a particular cast strategy, as well as the method of genetic algorithms for optimizing the strategy. Our technique uses dynamic reference knowledge of the area where the simulation takes place. Two reference sets were used: a steady-state field calculated with data collected from the Kiel University April 1982 hydrographic experiment, and data output from a regional quasigeostrophic model assimilating two years of Geosat altimetric data. The strategies obtained via the genetic algorithm method were compared w...
... In [21], the authors conducted a trial-and-error method to find the points to best reconstruct the so-called objective mapping for visualizing the data. After the introduction of the objective mapping technique, some studies have followed, focusing mainly on mapping-based optimization, which can compensate for the limitations of the trial-and-error method (e.g., [22][23][24]). Such prior studies designed arrays that can best reconstruct the spatial distribution by applying the optimization technique, such as the simulated annealing [22] and genetic algorithm [23] to minimize the covariance function or spatial averaged quadratic error [24]. ...
... After the introduction of the objective mapping technique, some studies have followed, focusing mainly on mapping-based optimization, which can compensate for the limitations of the trial-and-error method (e.g., [22][23][24]). Such prior studies designed arrays that can best reconstruct the spatial distribution by applying the optimization technique, such as the simulated annealing [22] and genetic algorithm [23] to minimize the covariance function or spatial averaged quadratic error [24]. Furthermore, many types of research have been performed to find the best objective mapping for the applications in diverse fields, such as mooring locations to measure the sea level altitudes [25], sensor arrays to monitor the oceanic meridional overturning circulation [26], and the collection data for the modeling with the data assimilation [27,28]. ...
... Most of the prior studies performed analyses mainly on the ideal case (e.g., [21][22][23]) or for the large-scale ocean (>5000 km) (e.g., [24,26]) rather than small-scale waters (<50 km) such as the coastal bays or estuaries, except [19]. In general, the spatial and temporal variabilities of hydrodynamic and water quality variables on the global-or large-scale seem to follow a more natural variation. ...
The semi-enclosed estuary is very susceptible to changes in the physical and environmental characteristics of the inflow from the land. Therefore, continuous and comprehensive monitoring of such changes is necessary for managing the estuary. Nevertheless, the procedure or framework has not been proposed appropriately to determine how many instruments are necessary and where they need to be monitored and standardized to detect critical changes. The present work proposes a systematical strategy for the deployments of the monitoring array by using the combination of graphical optimization with the objective mapping technique. In order to reflect the spatiotemporal characteristics of the bay, the representative variables and eigenvectors were determined by the Empirical Orthogonal Function (EOF), and the cosine angle among them calculated and used as a design index of optimization. At the recommended locations, the sampled representative variables were interpolated to reconstruct their spatiotemporal distribution and compared with the true distribution. The analysis confirmed that the selected locations, even with a minimal number of points, can be used for on-site monitoring. In addition, the present framework suggests how to determine installable regions for real-time monitoring stations, which reflect the global and local characteristics of the semi-enclosed estuary.
... [21] conducted a trial-and-error method to find the points to best reconstruct the so-called objective mapping for visualizing the data. After the introduction of the objective mapping technique, some researches have followed focusing mainly on mapping-based optimization, which can compensate for the limitation of the trial-end-error method (e.g., [22][23][24]). Such prior studies designed arrays that can best reconstruct the spatial distribution by applying optimization technique such as the simulated annealing ( [22]) and genetic algorithm ( [23]) to minimize the covariance function or spatial averaged quadratic error ( [24]). ...
... After the introduction of the objective mapping technique, some researches have followed focusing mainly on mapping-based optimization, which can compensate for the limitation of the trial-end-error method (e.g., [22][23][24]). Such prior studies designed arrays that can best reconstruct the spatial distribution by applying optimization technique such as the simulated annealing ( [22]) and genetic algorithm ( [23]) to minimize the covariance function or spatial averaged quadratic error ( [24]). Besides, many types of research have performed to find the best objective mapping for the applications to the diverse fields such as the mooring locations to measure the sea level altitudes ( [25]), the sensor arrays to monitor the oceanic meridional overturning circulation ( [26]), and the collection data for the modeling with the data assimilation ( [27,28]). ...
... Most of the prior studies performed analysis mainly on the ideal case (e.g., [21][22][23]) or for the large-scale ocean (>5000 km) (e.g., [24,26]) rather than small-scale waters (< 50 km) such as the coastal bays or estuaries except [19]. In general, the spatial and temporal variabilities of hydrodynamic and water quality variables in the global or large scales seem to follow more natural variation. ...
The semi-enclosed estuary is very susceptible to changes in the physical and environmental characteristics of the inflow from the land and the coastal sea weather and so the continuous and comprehensive monitoring is necessary for managing the estuary. Nevertheless, the standard procedure or schematic framework has not been proposed appropriately to determine how many instruments are necessary and where they need to be deployed to detect critical changes. Therefore, the present work proposes a systematical strategy for the deployments of the monitoring array by using the combination of the graphical optimization with the objective mapping technique. In order to reflect the spatiotemporal characteristics of the bay, the representative variables and eigenvectors are determined by the Empirical Orthogonal Function (EOF), and the cosine angle among them are calculated for a design index of optimization. At the recommended locations, the sampled representative variables are interpolated to reconstruct their spatiotemporal distribution and compared with the distributions of the true values. Analysis confirms that the selected locations, even with a small number of points, can be used for on-site monitoring. Also, the present framework suggests how to determine installable regions for real-time monitoring stations, which reflect the global and local characteristics of the semi-enclosed estuary.
... These facts require new strategies to deploy the Lagrangian observations distinct from those applicable to the standard Eulerian ones. Several theoretical studies [74,79] and numerical algorithms [45,18,80] have been developed to guide the drifter deployment by exploiting the geometric properties of the flow field. However, one of the major challenges in practice is that the exact underlying flow field is hard to obtain due to the intrinsic turbulent nature of the underlying flow field. ...
Deploying Lagrangian drifters that facilitate the state estimation of the underlying flow field within a future time interval is practically important. However, the uncertainty in estimating the flow field prevents using standard deterministic approaches for designing strategies and applying trajectory-wise skill scores to evaluate performance. In this paper an information measurement is developed to quantitatively assess the information gain in the estimated flow field by deploying an additional set of drifters. This information measurement is derived by exploiting causal inference. It is characterized by the inferred probability density function of the flow field, which naturally considers the uncertainty. Although the information measurement is an ideal theoretical metric, using it as the direct cost makes the optimization problem computationally expensive. To this end, an effective surrogate cost function is developed. It is highly efficient to compute while capturing the essential features of the information measurement when solving the optimization problem. Based upon these properties, a practical strategy for deploying drifter observations to improve future state estimation is designed. Due to the forecast uncertainty, the approach exploits the expected value of spatial maps of the surrogate cost associated with different forecast realiza-tions to seek the optimal solution. Numerical experiments justify the effectiveness of the surrogate cost. The proposed strategy significantly outperforms the method by randomly deploying the drifters. It is also shown that, under certain conditions, the drifters determined by the expected surrogate cost remain skillful for the state estimation of a single forecast realization of the flow field as in reality.
... It was shown that the optimal strategy for minimizing a certain norm of velocity error is to deploy the drifters at the center of different segments from a clustering algorithm [40]. In addition, genetic algorithms were applied, aiming to find the globally optimal drifter launch locations [41,42]. Other methods in determining the observational locations include exploiting certain low-order reconstructed fields [43,44] or placing the observations aligning with the most sensitive direction [45]. ...
Determining the optimal locations for placing extra observational measurements has practical significance. However, the exact underlying flow field is never known in practice. Significant uncertainty appears when the flow field is inferred from a limited number of existing observations via data assimilation or statistical forecast. In this paper, a new computationally efficient strategy for deploying Lagrangian drifters that highlights the central role of uncertainty is developed. A nonlinear trajectory diagnostic approach that underlines the importance of uncertainty is built to construct a phase portrait map. It consists of both the geometric structure of the underlying flow field and the uncertainty in the estimated state from Lagrangian data assimilation. The drifters are deployed at the maxima of this map and are required to be separated enough. Such a strategy allows the drifters to travel the longest distances to collect both the local and global information of the flow field. It also facilitates the reduction of a significant amount of uncertainty. To characterize the uncertainty, the estimated state is given by a probability density function (PDF). An information metric is then introduced to assess the information gain in such a PDF, which is fundamentally different from the traditional path-wise measurements. The information metric also avoids using the unknown truth to quantify the uncertainty reduction, making the method practical. Mathematical analysis exploiting simple illustrative examples is used to validate the strategy. Numerical simulations based on multiscale turbulent flows are then adopted to demonstrate the advantages of this strategy over some other methods.
... Three primary strategies have been used to assimilate surface drifters using the Lagrangian nature of the drifter device (i.e., consisting of position-time measurements). The first, denoted as the Eulerian approach (or "pseudo-Lagrangian"), converts a series of Lagrangian positions into Eulerian velocity by determining the change in drifter position over some time scale (Hernandez et al. 1995;Ishikawa et al. 1996;Toner et al. 2001a,b). This approach, in combination with assimilating temperature and salinity observations from other instruments, is straightforward to implement in existing operational ocean DA frameworks, and has been applied in many regions, such as the Gulf of Mexico Carrier et al. 2014Carrier et al. , 2016Muscarella et al. 2015;Coelho et al. 2015), the Indian Ocean (Santoki et al. 2012(Santoki et al. , 2013 and the Angola Basin (Phillipson and Toumi 2017). ...
Satellite-tracked in situ surface drifters, providing measurements of near-surface ocean quantities, have become increasingly prevalent in the global ocean observation system. However, the position data from these instruments are typically not leveraged in operational ocean data assimilation (DA) systems. In this work, the impact of an augmented-state Lagrangian data assimilation (LaDA) method using the Local Ensemble Kalman Transform Filter is investigated within a realistic regional ocean DA system. Direct positioning data of surface drifters released by the Consortium for Advanced Research on Transport of Hydrocarbon in the Environment during the summer 2012 Grand Lagrangian Deployment experiment are assimilated using a Gulf of Mexico (GoM) configuration of the Modular Ocean Model version 6 of the Geophysical Fluid Dynamics Laboratory. Multiple cases are tested using both 1/4° eddy-permitting and 1/12° eddy-resolving model resolutions: (1) a free running model simulation, (2) a conventional assimilation of temperature and salinity profile observations, (3) an assimilation of profiles and Lagrangian surface drifter positions, and (4) an assimilation of the profiles and derived Eulerian velocities. LaDA generally produces more accurate estimates of all fields compared to the assimilation of derived Eulerian velocities, with estimates of surface currents notably improving, when transitioning to 1/12° model resolution. In particular, LaDA produces the most accurate estimates of sea surface velocities under tropical cyclone conditions when hurricane Isaac (2012) impacted the GoM. Further experiments applying a vertical localization while assimilating surface drifter positions improves the estimates of temperature and salinity below the mixed layer depth. Cases including the surface drifter positions in the DA show better Lagrangian predictability than the conventional DA.
... In this study, the model provided the simulated data at selected observation locations, allowing for further statistical assessments of the proposed observation arrays. Studies were successively conducted afterwards to achieve better ocean mapping or estimation (Bennett and McIntosh, 1982;Bretherton et al., 1984;McIntosh, 1987;Barth and Wunsch, 1990;Barth, 1992;Hernandez et al., 1995). For example, by using model-simulated data and the optimal interpolation approach, the optimal observation configurations for mapping heat content change in the North Atlantic and seasonal variations of the 20°C isotherm in the equatorial Atlantic were investigated by Bretherton et al. (1984) and McPhaden et al. (1984), respectively. ...
Oceanic observation design is of considerable significance and has made remarkable progress during the past several decades. This study addresses the critical role of numerical modeling in oceanic observation design. Following a brief introduction of the characteristics of existing oceanic observation design studies, we present the advantages of the model-based observation design strategy and further review its decisive contribution. To demonstrate the effectiveness of this strategy, the targeted observation applications using the conditional nonlinear optimal perturbation (CNOP) approach for improving the Kuroshio predictions are introduced. Finally, the authors present their consideration for correcting model errors by targeted observations of sensitive model parameters and mitigating the model-dependency problem by utilizing multiple modeling systems. Suggestions on using observing system simulation experiments to validate the designed observations and extending the model-based observation design strategy into observing oceanic climatological mean states are also discussed.
Written by a group of international experts in their field, this book is a review of Lagrangian observation, analysis and assimilation methods in physical and biological oceanography. This multidisciplinary text presents new results on nonlinear analysis of Lagrangian dynamics, the prediction of particle trajectories, and Lagrangian stochastic models. It includes historical information, up-to-date developments, and speculation on future developments in Lagrangian-based observations, analysis, and modeling of physical and biological systems. Containing contributions from experimentalists, theoreticians, and modellers in the fields of physical oceanography, marine biology, mathematics, and meteorology, this book will be of great interest to researchers and graduate students looking for both practical applications and information on the theory of transport and dispersion in physical systems, biological modelling, and data assimilation.
Written by a group of international experts in their field, this book is a review of Lagrangian observation, analysis and assimilation methods in physical and biological oceanography. This multidisciplinary text presents new results on nonlinear analysis of Lagrangian dynamics, the prediction of particle trajectories, and Lagrangian stochastic models. It includes historical information, up-to-date developments, and speculation on future developments in Lagrangian-based observations, analysis, and modeling of physical and biological systems. Containing contributions from experimentalists, theoreticians, and modellers in the fields of physical oceanography, marine biology, mathematics, and meteorology, this book will be of great interest to researchers and graduate students looking for both practical applications and information on the theory of transport and dispersion in physical systems, biological modelling, and data assimilation.
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